Customers arrive at a service facility according to a Poisson process of rate λ customers/hour. Let X(t) be the number of customers that have arrived up to time t. Let W1,W2,... be the successive arrival times of the customers.
(a) Determine the conditional mean E[W1|X(t)=2].
(b) Determine the conditional mean E[W3|X(t)=5].
(c) Determine the conditional probability density function for W2, given that X(t)=5.
Answer:
Step-by-step explanation:
Given that:
X(t) = be the number of customers that have arrived up to time t.
[tex]W_1,W_2[/tex]... = the successive arrival times of the customers.
(a)
Then; we can Determine the conditional mean E[W1|X(t)=2] as follows;
[tex]E(W_!|X(t)=2) = \int\limits^t_0 {X} ( \dfrac{d}{dx}P(X(s) \geq 1 |X(t) =2))[/tex]
[tex]= 1- P (X(s) \leq 0|X(t) = 2) \\ \\ = 1 - \dfrac{P(X(s) \leq 0 , X(t) =2) }{P(X(t) =2)}[/tex]
[tex]= 1 - \dfrac{P(X(s) \leq 0 , 1 \leq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}[/tex]
[tex]= 1 - \dfrac{P(X(s) \leq 0 ,P((3 \eq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}[/tex]
Now [tex]P(X(s) \leq 0) = P(X(s) = 0)[/tex]
(b) We can Determine the conditional mean E[W3|X(t)=5] as follows;
[tex]E(W_1|X(t) =2 ) = \int\limits^t_0 X (\dfrac{d}{dx}P(X(s) \geq 3 |X(t) =5 )) \\ \\ = 1- P (X(s) \leq 2 | X (t) = 5 ) \\ \\ = 1 - \dfrac{P (X(s) \leq 2, X(t) = 5 }{P(X(t) = 5)} \\ \\ = 1 - \dfrac{P (X(s) \LEQ 2, 3 (t) - X(s) \leq 5 )}{P(X(t) = 2)}[/tex]
Now; [tex]P (X(s) \leq 2 ) = P(X(s) = 0 ) + P(X(s) = 1) + P(X(s) = 2)[/tex]
(c) Determine the conditional probability density function for W2, given that X(t)=5.
So ; the conditional probability density function of [tex]W_2[/tex] given that X(t)=5 is:
[tex]f_{W_2|X(t)=5}}= (W_2|X(t) = 5) \\ \\ =\dfrac{d}{ds}P(W_2 \leq s | X(t) =5 ) \\ \\ = \dfrac{d}{ds}P(X(s) \geq 2 | X(t) = 5)[/tex]
Rule double the last number number number than add 3
2. 7 17 _ _
Answer:
[tex]37[/tex]
[tex]77[/tex]
Step-by-step explanation:
[tex]17 \times 2 +3=37\\37 \times 2 +3=77[/tex]
Answer:
37 77
Step-by-step explanation:
2(17) + 3 = 37
2(37) + 3 = 77
Your utility company charges 11 cents per kilowatt-hour of electricity. Complete parts (a) and (b) below. a. What is the daily cost of keeping lit a 75-watt light bulb for 12 hours each day? b. How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light using only 20 watts of power?
Answer:
a. 9.9 cents
b. 26.5 dollars
Step-by-step explanation:
The first thing they mention to us is the cost of energy 11 cents / kwh
a) In the first point they ask us to calculate the daily cost of keeping the flashlight on for 12 hours, they tell us that it consumes 75 watts per hour, but this value must be passed to kW because the cost is given in kWh
to pass it, it would be: 75 watt * 1 kw / 1000 watt = 0.075 kw,
the formula to apply would be like this:
Daily cost = flashlight cost * time * energy cost
we all know them so we replace:
Daily cost = 0.075 kw * 12 h * 11 cents / kwh = 9.9 cents
b) Now, to know the annual savings, we must calculate the difference between the expense of the normal flashlight and the LED, let's calculate the daily cost of the LED, like this:
20 watt * 1 kw / 1000 watt = 0.02 kw
Daily cost = 0.02 kw * 12 h * 11 cents / kwh = 2.64 cents
Now by calculating the difference we multiply by 365 which are the days of a year.
Savings / year = (9.9 - 2.64) * 365 = 2649.9 cents = 26.5 dollars.
An aquarium in the shape of a right rectangular prism is 12.5 inches long, 6 inches wide and 8 inches high. What is the total amount of water needed, to the nearest cubic inch, to fill 90% of the aquarium with water?
Answer:
The total amount of water needed is 540 cubic inches.
Step-by-step explanation:
A cubic prism has three dimension. Lenght l, width w and height h.
It's volume is:
[tex]V = l*w*h[/tex]
In this question:
[tex]l = 12.5, w = 6, h = 8[/tex]
Dimensions in inches, so the volume will be in cubic inches.
[tex]V = 12.5*6*8 = 600[/tex]
The volume is 600 cubic inches.
What is the total amount of water needed, to the nearest cubic inch, to fill 90% of the aquarium with water?
This is 90% of 600. So
0.9*600 = 540
The total amount of water needed is 540 cubic inches.
A radio station dedicates 20% of their air time to commercials for each radio show. During a radio show, 30 minutes of commercials played. How long was the radio show?
Answer:
150 minutes (2.5 hours)
Step-by-step explanation:
We must consider that the total time that the radio program lasted represents the 100%.
Of that 100% we are told that 20% is dedicated to commercials. So the 30 minutes of commercials correspond to 20% of the air time, which can be represented in the following table:
Percentage of time time
20% ⇒ 30min
and we are looking for how long the show was on the air (the 100%).
So updating the table( I will call x the total time on the air):
Percentage of time time
20% ⇒ 30min
100% ⇒ x
This reationship between three values can be solve by the rule of three: multiply the cross quantities on the table (100 by 30) and divide by the remaining amount (20):
x = 100*30 / 20
x= 3000 / 20
x = 150 minutes
The radio show was 150 minutes (2.5 hours) long.
The population of a city in Texas is about 1,030,000. The population of the city in t years can be predicted using the equation P = 1,030,000(1.12)t. According to this equation, what will the approximate population of the city be in 9 years? 10,382,400
Answer:
2,856,271
Step-by-step explanation:
We presume your equation is intended to be ...
P = 1,030,000(1.12)^t
To find the prediction in 9 years, put 9 where t is and do the arithmetic.
P = 1030000(1.12^9) ≈ 2,856,271
In 9 years, the population is predicted to be about 2,856,271.
Answer:
To predict the population in nine years, substitute 9 for t in the equation and simplify:
P = 1,030,000(1.12)9
= 1,030,000 ∙ 2.77
= 2,853,100.
Step-by-step explanation:
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. 1. Suppose a sample of 955 tenth graders is drawn. Of the students sampled, 812 read above the eighth grade level. Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. 2. Suppose a sample of 955 tenth graders is drawn. Of the students sampled, 812 read above the eighth grade level. Using the data, construct the 90% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.
Answer:
The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:
[tex] \hat p =\frac{955-812}{955}= 0.150[/tex]
[tex]0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131[/tex]
[tex]0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169[/tex]
And the 90% confidence interval would be given (0.131;0.169).
Step-by-step explanation:
We have the following info given:
[tex]n= 955[/tex] represent the sampel size slected
[tex] x = 812[/tex] number of students who read above the eighth grade level
The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:
[tex] \hat p =\frac{955-812}{955}= 0.150[/tex]
The confidence interval for the proportion would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 90% confidence interval the significance is [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex], with that value we can find the quantile required for the interval in the normal standard distribution and we got.
[tex]z_{\alpha/2}=1.64[/tex]
And replacing into the confidence interval formula we got:
[tex]0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131[/tex]
[tex]0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169[/tex]
And the 90% confidence interval would be given (0.131;0.169).
The diagram shown represents a garden. The scale is 2/3 centimeters for every 3 1/2 meters. Each square in the drawing measures 1cm by 1cm. Find the actual length, width and area of the garden based upon the given drawing.
Answer:
Length = [tex]\frac{189}{4}\ m[/tex]
Width = 21 m
Area of garden = 992.25 [tex]m^{2}[/tex]
Step-by-step explanation:
Side of square = 1 cm
As per the given question figure, we can see that there are 11 square across the length of rectangular garden.
But the garden includes only 9 squares, the corner squares are not in the garden.
So, length of garden = 9 [tex]\times[/tex] 1 = 9 cm
Using the scaling given in the question,
[tex]\dfrac{2}{3}\ cm = 3\dfrac{1}{2}\ m\\[/tex][tex]\Rightarrow \dfrac{2}{3}\ cm = \dfrac{7}{2}\ m[/tex]
[tex]1 cm = \dfrac{\dfrac{7}{2}}{\dfrac{2}{3}} \ m \Rightarrow \dfrac{21}{4}\ m[/tex]
So, length of garden = [tex]\dfrac{21}{4} \times 9 \Rightarrow \dfrac{189}{4}\ m[/tex]
-------------
And, similarly width contains 4 squares, (Corner squares are excluded)
Width of garden = [tex]\dfrac{21}{4} \times 4 \Rightarrow 21\ m[/tex]
-------------
Area of garden = Length [tex]\times[/tex] Width
[tex]\Rightarrow \dfrac{189}{4} \times 21\\\Rightarrow \dfrac{3969}{4}\\\Rightarrow 992.25\ m^{2}[/tex]
There were 227 Kindergarteners who wanted a sticker. Stickers came in
books of 25. How many books of stickers did the school need to buy?
a) 25 books of stickers
b)10 books of stickers
c) 9books of stickers
d) 5 books of stickers
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 32% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below.
a. Find the probability that both generators fail during a power outage (Round to four decimal places as needed.)
b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed. (Round to four decimal places as needed.)
Answer:
a. 0.1024
b. 0.8976
Step-by-step explanation:
The probability that x generators don't fail when they are needed follows a binomial distribution, because we have n identical and independent events (2 backup generators) with a probability p of success (1-0.32=0.68) and a probability q of failure (0.32).
So, the probability that x generator success are calculated as:
[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*q^{n-x}\\P(x)=\frac{2!}{x!(2-x)!}*0.68^{x}*0.32^{2-x}[/tex]
Then, the probability that both generators fail during a power outage is equal to the probability that 0 generators success. It is calculated as:
[tex]P(0)=\frac{2!}{0!(2-0)!}*0.68^{0}*0.32^{2-0}=0.1024[/tex]
At the same way, the probability of having a working generator in the event of a power outage is equal to the probability that at least 1 generator success. It is calculated as:
[tex]P(x\geq1)=P(1)+P(2) \\P(1)=\frac{2!}{1!(2-1)!}*0.68^{1}*0.32^{2-1}=0.4352\\P(2)=\frac{2!}{2!(2-2)!}*0.68^{2}*0.32^{2-2}=0.4624\\P(x\geq1)=0.4352+0.4624=0.8976[/tex]
This probability is not high enough for the hospital, both generators fail approximately the 10% of the time when needed.
On Monday, Richard worked for 4 hours and earned $36. On Tuesday, Richard worked for 6 hours and earned $54. On Wednesday, Richard worked for 5 hours and earned $45.
Answer:
Richard works for $9 per hour
Step-by-step explanation:
Answer:
The answer is proportional. He makes 9$ an hour
Step-by-step explanation:
Your welcome
Please answer this question !! Thank you !! Will give brainliest !!
Answer:
m = 1/4
Step-by-step explanation:
We want to get the equation in slope intercept form
y = mx+b where m is the slope and b is the y intercept
x -4y +3 =0
Add 4y to each side
x -4y+3 +4y = 0+4y
x-3 = 4y
Divide each side by 4
1/4x -3/4 =y
the slope is 1/4 and the y intercept is -3/4
Using the critical value rule, if a two-sided null hypothesis cannot be rejected for a single mean at a given significance level, then the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ______________ be rejected at the same significance level.
Answer:
If the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.
Step-by-step explanation:
When we performed a two-sided test and the null hypothesis failed to be rejected, when we perform a one-sided test we may reject or not the null hypothesis.
For instance, we have a 5% significance level test, where the test statistic is z=1.8.
For a two-sided test the critical values for α=5% are zc=±1.960. In this situation, the null hypothesis failed to be rejected.
But if we perform a one-sided test with the same significance level, we have a critical value z=1.645 and the conclusion is that the null hypothesis is rejected.
Then, if the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.
We are only sure that if a two-sided test rejects the null hypothesis, a one-side test with same significance level will always reject the null hypothesis.
WILL MARK BRAINLIEST
Teah was selling candy bars for a fundraiser. She spent $25 on a box of candy bars and sold each candy bar for $2.50. Her profit was $75. Teah wrote the equation 2.5c - 25 = 75 for this situation, and she found c = 40. Which statement is true about the solution c = 40?
A) The solution c = 40 is the number of candy bars Teah sold.
B) The solution c = 40 is the profit in dollars Teah made from each candy bar.
C) The solution c = 40 is the amount in dollars that Teah spent on a box.
D) The solution c = 40 is the selling cost of a box of candy bars, in dollars.
E) The solution c = 40 is the selling cost of each candy bar, in dollars.
Answer:
A
Step-by-step explanation:
You can substitute 40 into c, work out the equation and you'll get $75 as the profit. Each candy bar is $2.5 so c would be the number of candy bars she sold.
What is the value of y???? I NEED ANSWERS!!!! Please and thank you!!!
Answer:68
Step-by-step explanation:
angle sum property
56+y+y-12=180
44+2y=180
2y=180-44=136
y=136/2
=68
VERIFICATION :56+68+56
=180
Y =112°
remember the sum of angles in a triangle equals 180°
EDIT : previous answer is right, i messed up with the sign
Aaron is a biologist who wants to determine the growth rate of a strain of bacteria. Aaron places 1450 bacteria into a controlled environment and waits 6 hours. When Aaron checks 6 hours later, there are now 3592 bacteria. What is the hourly growth rate of the bacteria?
Answer:
Roughly 15% hourly rate.
Step-by-step explanation:
This is an exponential function that relates to natural growth.
Use the formula A = P*e^(rt)
I have attached the work to your problem.
Please see the attachment below.
I hope this helps!
A light bulb consumes 15300 watt-hours in 4 days and 6 hours . How many watt-hours does it consume per day?
Answer:
3600
Step-by-step explanation:
It consumes 3600 watt hours per day. Steps are included below.
We know that there is 24 hours in a day so we times 24 by the consumes watt hours that is 15300. So 24 times 15300. After that we need to time 4 times 24+6 = the answer that is 3600. That how you get the answer.
Steps:
1: 24*15300/(4*24+6)=3600
Answer: 3600 watt hours per day
Hope this helps.
Answer:
3,600
Step-by-step explanation:
In the question, there is energy consumption and a rate but not in an easy way.
In order to find out how much watt-hours the light bulb consumes per day, the easiest way is to multiply by the hour to find out how much it uses in a day.
In 4 days and 6 hours there are 102 hours.
[tex]4 \times 24 = 96[/tex]
[tex]96 + 6 = 102[/tex]The hours for 4 days...
[tex]96 + 6 = 102[/tex]
4 days plus 6 hours. The total time...
Now make the watt-hours usage an hourly rate...
[tex]15300 + 102 = 150[/tex]
150 watts/hour...
Take the hourly rate and multiply it by 24 (number of hours in a day) to find out how many watt-hours the lightbulb uses in a day...
[tex]150 \times 24 = 3600[/tex]
Which of the following could represent the graph of f(x)=x^4+x^3-8x^2-12x
Answer:
Plot f(x)=x^4+x^3-8x^2-12x
Step-by-step explanation:
With a height of 68 in, Nelson was the shortest president of a particular club in the past century. The club presidents of the past century have a mean height of 70.7 in and a standard deviation of 2.3 in. a. What is the positive difference between Nelson's height and the mean? b. How many standard deviations is that [the difference found in part (a)]? c. Convert Nelson's height to a z score. d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Nelson's height usual or unusual?
Answer:
a. The positive difference between Nelson's height and the population mean is: [tex] \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in[/tex].
b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).
c. Nelson's z-score: [tex] \\ z = -1.1739 \approx -1.174[/tex] (Nelson's height is below the population's mean 1.174 standard deviations units).
d. Nelson's height is usual since [tex] \\ -2 < -1.174 < 2[/tex].
Step-by-step explanation:
The key concept to answer this question is the z-score. A z-score "tells us" the distance from the population's mean of a raw score in standard deviation units. A positive value for a z-score indicates that the raw score is above the population mean, whereas a negative value tells us that the raw score is below the population mean. The formula to obtain this z-score is as follows:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
[tex] \\ z[/tex] is the z-score.
[tex] \\ \mu[/tex] is the population mean.
[tex] \\ \sigma[/tex] is the population standard deviation.
From the question, we have that:
Nelson's height is 68 in. In this case, the raw score is 68 in [tex] \\ x = 68[/tex] in.[tex] \\ \mu = 70.7[/tex]in.[tex] \\ \sigma = 2.3[/tex]in.With all this information, we are ready to answer the next questions:
a. What is the positive difference between Nelson's height and the mean?
The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):
[tex] \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in[/tex].
That is, the positive difference is 2.7 in.
b. How many standard deviations is that [the difference found in part (a)]?
To find how many standard deviations is that, we need to divide that difference by the population standard deviation. That is:
[tex] \\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174[/tex]
In words, the difference found in part (a) is 1.174 standard deviations from the mean. Notice that we are not taking into account here if the raw score, x, is below or above the mean.
c. Convert Nelson's height to a z score.
Using formula [1], we have
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{68\;in - 70.7\;in}{2.3\;in}[/tex]
[tex] \\ z = \frac{-2.7\;in}{2.3\;in}[/tex]
[tex] \\ z = -1.1739 \approx -1.174[/tex]
This z-score "tells us" that Nelson's height is 1.174 standard deviations below the population mean (notice the negative symbol in the above result), i.e., Nelson's height is below the mean for heights in the club presidents of the past century 1.174 standard deviations units.
d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Nelson's height usual or unusual?
Carefully looking at Nelson's height, we notice that it is between those z-scores, because:
[tex] \\ -2 < z_{Nelson} < 2[/tex]
[tex] \\ -2 < -1.174 < 2[/tex]
Then, Nelson's height is usual according to that statement.
15. The solutions to (x+4)2 - 2 = 7 are
1) -4+ 5
3) -1 and -7
2) 4+ 5
4) 1 and 7
I
Answer:
Step-by-step explanation:
(x + 4)^2 - 2 = 7 simplifies to
(x + 4)^2 = 5
We must isolate x. To do this, take the square root of both sides, obtaining:
x + 4 = ±√5
There are two roots/solutions. They are:
x = -4 + √5 and x = -4 - √5
You must include the square root operator (√). Use " ^ " to denote exponentiation.
The solutions to the given equation (x + 4)² - 2 = 7 when calculated are; 1 and 7
How to Solve Algebra Problems?We are given the equation as;
(x + 4)² - 2 = 7
Add 2 to both sides to get;
(x + 4)² = 9
Find the square root of both sides to get;
x + 4 = ±3
Thus;
x = 3 + 4 and x = -3 + 4
x = 1 and 7
Read more about Algebra at; https://brainly.com/question/4344214
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What is the solution to this equation
Answer:
x=-10
Step-by-step explanation:
x+8=-2
x=-10 (Subtract 8)
Answer:
-10
Step-by-step explanation:
1. Write it out.
x+8=-2
2. Get x by itself.
To do this, we have to move the 8, but to do that that we have to move it to the other side of the equation. Because the opposite of addition is subtraction, we have to subtract 8 by both sides. x+8=-2
-8 -8
x=-10
And that's the answer! Hope this helped :)
What value of x is in the solution set of 2(3x - 1) = 4x - 6?
-10
-5
OOO
Sample Response: Distance is a function of time. The constant rate of change is 64. Write
the equation Y=64x + 22. Substitute 4 in for x to get 278 miles,
Compare your response to the sample response above. Did your explanation
include that distance is a function of time?
include that the constant rate of change, or slope, is 64?
include the equation y = 64x + 22?
say to substitute 4 in for x to get 278 miles?
Answer:
Yes the explanation satisfy the questions stated.
See below for explanation
Step-by-step explanation:
From the question, distance is said to be a function of time and the constant rate of change is 64.
y = 64x + 22
The above is in the form of a Linear equation:
y = mx + c
Where y = dependent variable (distance)
x = independent variable (time)
m = slope = distance/time
c = constant = 22
m = constant rate of change = 64
If x (time) = 4
y (distance) = 278 miles
y = 64(4) + 22
y = 256 + 22
y = 256 + 22
y = 278 miles
Answer:
nclude that distance is a function of time?
include that the constant rate of change, or slope, is 64?
include the equation y = 64x + 22?
say to substitute 4 in for x to get 278 miles?
Step-by-step explanation:
Help please. help please. Below please
Answer:
x = 30pitch = 7Step-by-step explanation:
If you draw a horizontal line through the shaded triangle such that it intersects the left vertex, you see that it bisects the 60° angle at that vertex. The measure of x is the same as the measure of either half of that bisected angle, so is 30°.
The pitch associated in the table with an angle of 30° is 7.
x = 30pitch = 7A line passes through the point (-4,6) and has a slope of -5. Write an equation in point-slope form for this line.
Answer:
hope this helps you
Data collected over an extended period of time show that women college soccer players have a relatively high rate of concussions, often with life-changing consequences. See Stanford Star Retires and Concussions Derail Promising Careers. For collegiate women soccer players the concussion rate is .63 per 1,000 participation hours (practice and game participation hours), for collegiate men soccer players the concussion rate is .41 per 1,000 participation hours (the concussion rate in college football is .61 per 1,000 participation hours). Use the Poisson distribution to answer the following questions.
a. What is the probability that the men's team experiences 2 or more concussions? (Use 3 decimal places).
b. What is the probability that the women's team experiences 2 or more concussions? (Use 3 decimal places).
The probability that the women's team experiences 2 or more concussions is 0.0013.
We are given that;
The concussion rate = 0.63 per 1,000 participation hours
Now,
The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space when these events occur with a known average rate and independently of the time since the last event.
The probability mass function of the Poisson distribution is given by:
[tex]$P(X=k)=\frac{\lambda^k e^{-\lambda}}{k!}$[/tex]
where X is the number of events occurring in the interval, k is a non-negative integer, and λ is the average rate of events per interval.
a. For collegiate men soccer players, the concussion rate is .41 per 1,000 participation hours.
Therefore, the average number of concussions per hour is λ = 0.41/1000 = 0.00041.
Let X be the number of concussions experienced by the men's team in an hour. Then X follows a Poisson distribution with parameter λ = 0.00041. We want to find P(X ≥ 2). Using the Poisson distribution formula,
[tex]$P(X \geq 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)$$= 1 - \frac{0.00041^0 e^{-0.00041}}{0!} - \frac{0.00041^1 e^{-0.00041}}{1!}$$= 1 - e^{-0.00041}(1 + 0.00041)$$\approx \boxed{0.0002}$[/tex]
b. For collegiate women soccer players, the concussion rate is .63 per 1,000 participation hours.
Therefore, the average number of concussions per hour is λ = 0.63/1000 = 0.00063.
Let Y be the number of concussions experienced by the women's team in an hour. Then Y follows a Poisson distribution with parameter λ = 0.00063. We want to find P(Y ≥ 2). Using the Poisson distribution formula,
[tex]$P(Y \geq 2) = 1 - P(Y < 2) = 1 - P(Y = 0) - P(Y = 1)$$= 1 - \frac{0.00063^0 e^{-0.00063}}{0!} - \frac{0.00063^1 e^{-0.00063}}{1!}$[/tex]
[tex]$= 1 - e^{-0.00063}(1 + 0.00063)$[/tex]
[tex]$\approx \boxed{0.0013}$[/tex]
Therefore, by poisson distribution formula answer will be 0.0013.
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a study shows that, over the course of a lifetime, the average salary of college graduates is greater than the salary of people with only a high school diploma. The results were published claiming that graduating from college ensures you will make more money of the course of you lifetime. What is the problem with reporting results this way?
Answer:
Answer: The word "ensures" implies that it is certain.
In the case of the study, they simply found that the average salary is greater for college graduates. This doesn't mean that in every case the college graduate makes more money.
The problem is the word "ensures". Our study doesn't show certainty only a general pattern.
Step-by-step explanation:
There are many cones with a volume of 72pi cubic inches. For example, one such cone could have a radius of 6 inches and a height of 6 inches.
Find another possible pair of measurements (radius and height) to make the same volume. (EXTRA CREDIT for each additional pair that you find.)
Answer:
Step-by-step explanation:
The volume of a cone of height h and circular base of radius r, is [tex] V = \frac{\pi r^2 h}{3}[/tex]. In this case we have that [tex]V=72\pi[/tex].Then, we have that
[tex]72\pi = \frac{\pi r^2 h}{3}[/tex]
multiplying by 3 on both sides and dividing by [tex]\pi[/tex] we have that
[tex]216 = r^2\cdot h[/tex]
Suppose that we know the value of r, then we can find the value of h by solving h, that is
[tex] h = \frac{216}{r^2}[/tex].
So, by choosing any positive value of r, we can find the value for h. Note that if r=6, then [tex]h= \frac{216}{6^2} = 6[/tex]. This means that the amount of credit is infinite :)
In the months leading up to an election, news organizations conduct many surveys to help predict the results of the election. Often news organizations will increase the sample size in the last few weeks before the election. Which of the following is the primary reason they increase the sample size?
A. A larger sample size gives a narrower confidence interval.
B. A larger sample size allows more people to give their input.
C. A larger sample size gives a higher confidence level.
D. A larger sample size means the sampling method isn’t as important.
Answer:
A. A larger sample size gives a narrower confidence interval.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
As the sample size increases(n increases), the margin of error decreases, given a narrower, more precise confidence interval.
So the correct answer is:
A. A larger sample size gives a narrower confidence interval.
Help....!! I need to solve this simultaneous equation y=x-2 and y=3x+5 With working out if possible please....
Step-by-step explanation:
Y= x - 2. Y = 3x + 5
Putting value of y
x - 2 = 3x + 5
-2 - 5 = 3x - x
-7 = 2x
-7/2 = x
Putting value of x
Y = 3(-7/2) + 5
Y = - 10.5 + 5
Y = - 5.5
