Answer:
[tex]f ( t ) = 3.7*sin ( 0.01736*t ) + 12[/tex]
Step-by-step explanation:
Solution:-
- We are to model a sinusoidal function for the number of hours of daylight measured in one year in Ellenville.
- We will express a general form of a sinusoidal function [ f ( t ) ] as follows:
[tex]f ( t ) = A*sin ( w*t ) + c[/tex]
Where,
A: The amplitude of the hours of daylight
w: The angular frequency of occurring event
c: The mean hours of daylight
t: The time taken from reference ( days )
- We are given that the longest day [ [tex]f ( t_m_a_x )[/tex] ] occurred on June 21st and the shortest day [ [tex]f ( t_m_i_n )[/tex] ] on December 21st.
- The mean hours of daylight ( c ) is the average of the maximum and minimum hours of daylight as follows:
[tex]c = \frac{f(t_m_a_x ) +f(t_m_i_n ) }{2} \\\\c = \frac{15.7 + 8.3}{2} = \frac{24}{2} \\\\c = 12[/tex]
- The amplitude ( A ) of the sinusoidal function is given by the difference of either maximum or minimum value of the function from the mean value ( c ):
[tex]A = f ( t_m_a_x ) - c\\\\A = 15.7 - 12\\\\A = 3.7[/tex]
- The frequency of occurrence ( w ) is defined by the periodicity of the function. In other words how frequently does two maximum hours of daylight occur or how frequently does two minimum hours of daylight occur.
- The time period ( T ) is the time taken between two successive maximum duration of daylight hours. We were given the longest day occurred on June 21st and the shortest day occurred on December 21st. The number of days between the longest and shortest day will correspond to half of the time period ( 0.5*T ):
[tex]0.5*T = 7 + 31 + 31 + 30 +31 +30 +21\\\\T = 2* [ 181 ] \\\\T = 362 days[/tex]
- The angular frequency ( w ) is then defined as:
[tex]w = \frac{2\pi }{T} = \frac{2\pi }{362} \\\\w = 0.01736[/tex]
- We will now express the model for the duration of daylight each day as function of each day:
[tex]f ( t ) = 3.7*sin ( 0.01736*t ) + 12[/tex]
What is the coefficient of the term x5y7 in the expansion of (x - y)12 ?
Answer:
12 and -12
Step-by-step explanation:
12x-12y is the expansion using the distributive property, so the coefficient of x is 12 and the coefficient of y is -12
A parabola can be drawn given a focus of (5, 10) and a directrix of y= -2. what can be said about the parabola?
the parabola has a vertex at (_,_), has a low-value of _ and it opens __.
Answer:
(5, 4)4upwardStep-by-step explanation:
The directrix is a horizontal line (y=-2). The parabola will open in the direction the focus is from the directrix. Here, the y-coordinate of the focus is 10, so the focus is above the directrix and the parabola opens upward.
The vertex is halfway between the directrix and the focus, so has y-coordinate ...
(-2 +10)/2 = 4
Since the parabola opens upward, the vertex is a minimum (the "low value"). Its x-coordinate is the same as that of the focus, so the vertex is (5, 4).
The parabola has a vertex at (5, 4), has a low value of 4, and it opens upward.
A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that your team scored at an average of less than 110 points in the years 2013-2015. Test this claim at a 1% level of significance. For this test, assume that the population standard deviation for relative skill level is unknown.
1. Calculate and print the mean points scored by your team during the years you picked.
2. Identify the mean score under the null hypothesis. You only have to identify this value and do not have to print it.
3. Assuming that the population standard deviation is unknown, use Python methods to carry out the hypothesis test.
4. Calculate and print the test statistic rounded to two decimal places.
5. Calculate and print the P-value rounded to four decimal places.
Answer:
1. M=108
2. μ=110
3. In the explanation.
4. Test statistic t = -1.05
5. P-value = 0.1597
Step-by-step explanation:
The question is incomplete: to solve this problem, we need the sample information: size, mean and standard deviation.
We will assume a sample size of 10 matches, a sample mean of 108 points and a sample standard deviation of 6 points.
1. The mean points is the sample points and has a value of 108 points.
2. The null hypothesis is H0: μ=110, meaning that the mean score is not significantly less from 110 points.
3. This is a hypothesis test for the population mean.
The claim is that the mean score is significantly less than 110.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu< 110[/tex]
The significance level is 0.05.
The sample has a size n=10.
The sample mean is M=108.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6}{\sqrt{10}}=1.9[/tex]
4. Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{108-110}{1.9}=\dfrac{-2}{1.9}=-1.05[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
5. This test is a left-tailed test, with 9 degrees of freedom and t=-1.05, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.05)=0.1597[/tex]
As the P-value (0.1597) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean score is significantly less than 110.
Nicole has x beads. Together we have 56 beads. How many beads will I have if I lose 1/4 of my beads?
Answer:
(56 - x) * 3/4
Step-by-step explanation:
x + y = 56
y = 56 - x
y' = (56 - x) * 3/4
The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 24 minutes and a standard deviation of 7 minutes. Find the probability that a randomly selected athlete uses a stairclimber for
(a) less than 19 minutes,
(b) between 24 and 33 minutes, and
(c) more than 40 minutes.
Which event is unusual?
Answer:
(a) The probability that a randomly selected athlete uses a stairclimber for less than 19 minutes is 0.2388.
(b) The probability that a randomly selected athlete uses a stairclimber for between 24 and 33 minutes is 0.3997.
(c) The probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is 0.0113.
Step-by-step explanation:
We are given that the amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 24 minutes and a standard deviation of 7 minutes.
Let X = amounts of time per workout an athlete uses a stairclimber
So, X ~ Normal([tex]\mu=24,\sigma^{2} =7^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time = 24 minutes
[tex]\sigma[/tex] = standard deviation = 7 minutes
(a) The probability that a randomly selected athlete uses a stairclimber for less than 19 minutes is given by P(X < 19 minutes)
P(X < 19 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{19-24}{7}[/tex] ) = P(Z < -0.71) = 1 - P(Z [tex]\leq[/tex] 0.71)
= 1 - 0.7612 = 0.2388
The above probability is calculated by looking at the value of x = 0.71 in the z table which has an area of 0.7612.
(b) The probability that a randomly selected athlete uses a stairclimber for between 24 and 33 minutes is given by = P(24 min < X < 33 min)
P(24 min < X < 33 min) = P(X < 33 min) - P(X [tex]\leq[/tex] 24 min)
P(X < 33 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{33-24}{7}[/tex] ) = P(Z < 1.28) = 0.8997
P(X [tex]\leq[/tex] 24 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{24-24}{7}[/tex] ) = P(Z [tex]\leq[/tex] 0) = 0.50
The above probability is calculated by looking at the value of x = 1.28 and x = 0 in the z table which has an area of 0.8997 and 0.50 respectively.
Therefore, P(24 min < X < 33 min) = 0.8997 - 0.50 = 0.3997
(c) The probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is given by P(X > 40 minutes)
P(X > 40 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{40-24}{7}[/tex] ) = P(Z > 2.28) = 1 - P(Z [tex]\leq[/tex] 2.28)
= 1 - 0.9887 = 0.0113
The above probability is calculated by looking at the value of x = 2.28 in the z table which has an area of 0.9887.
The event of probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is unusual because this probability is less than 5% and any even whose probability is less than 5% is said to be unusual.
You've found yourself trapped in a desert, desperate for a drink of water. Amazingly, you come across a food cart right there and they have glasses of water available for just $1! You even have a dollar! You're all set. Except the cart vendor tells you He only sells 80z glasses of water, and he only have 6oz and 10oz glasses. "I'll pay a dollar for the 6oz!" you say. "No," he replies, "I won't be cheating you." How can you use the 6oz glass and the 10oz glass to measure out exactly 8oz?
If I'm understanding the problem correctly, the vendor sells water in exactly 8 oz increments, but only has glasses that can hold 6 oz or 10 oz.
Fill up the 10 oz glass, then (carefully) pour its contents into a 6 oz glass until it it is full. Then the 10 oz glass should contain 4 oz of water. Drink the 4 oz, repeat this process to get your 8 oz, and pay the man.
how and explain how to find the value of x . step by step I will give the most correct one the brainiest
Answer:
X=96
Step-by-step explanation:
180-134=46
180-130=50
SUM OF TWO INTERIOR ANGLES = EXTERIOR ANGLE
50 + 46=96
Which phrase represents the algebraic expression 3d+7?
Answer:
3 multiplied by a variable d and add seven to it
Step-by-step explanation:
3 multiplied by a variable d and add seven to it.
Choose an appropriate metric unit for the capacity of a bottle of ink.
2. Find the measure of angle G. Round your answer to the nearest degree.
Answer:
G = 53 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin G = 24/30
Take the inverse sin of each side
sin ^-1 sin G = sin ^-1 (24/30)
G =53.13010235
To the nearest degree
G = 53 degrees
Find the measure of an angle whose supplement measures five times its measure.
The angle measure ___ degrees.
Answer:
30°
Step-by-step explanation:
supplementary angles are two sets of angles whose sum form 180°
According to the problem, one set equals 5 times the other.
Let the other be x,
It means it's compliment is 5x;
It means therefore that ;
x + 5x = 180°
6x = 180°;
x = 180°/ 6 = 30°;
Therefore the angle measures 30° and it's supplement 150°.
11. Little Sally Walker has a choice between going to an in-state college where she would pay
$3,500 per year for tuition or an out of state college where she would pay $6,000 per year. The
cost of living at the in-state college is $700 per month in rent. The out of state college is $400
per month in rent. Assuming all the other factors are equal,
a. what is the yearly expense of the in-state college?
b. what is the yearly expense of the out-of-state college?
Answer:
Step-by-step explanation:
Lets calculate first for in state college
yearly tuition fees = $3,500
monthly living expense = $700
one year has 12 months so yearly living expense =$700 * 12 = $8,400
Yearly expense of the in state college = yearly tuition fees ($3,500 )+ yearly living expense($8,400) = $3,500 + $8,400 = $11,900
____________________________________________________
Lets calculate first for out of state college
yearly tuition fees = $6,000
monthly living expense = $400
one year has 12 months so yearly living expense =$400 * 12 = $4,800
Yearly expense of the out of state college = yearly tuition fees ($3,500 )+ yearly living expense($8,400) = $6,000 + $4,800 = $10,800
____________________________________________________
Plot the image of point A under a reflection across the
y-axis.
Answer:
(-2,5)
Step-by-step explanation:
A reflection across the y axis (x,y)→(−x,y)
Point A is at (2,5) so it becomes (-2,5)
Answer:
(-2,5)
a reflection across the y axis causes for it to basically be reversed along the y axis. meaning if it is at (2,5) then it will be (-2,5)
find the pattern then find the next term of the sequence. 5, 1, 7, 0, 9, -1, 11
Answer:
5, 1, 7, 0, 9, -1, 11, -2, 13
Step-by-step explanation:
5, 1, 7, 0, 9, -1, 11
Two series in one:
5, 7, 9, 11, 131, 0, -1, -2Two cyclists, 112 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other, and they meet after 4 hours of riding.
a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.
b. What are the speeds of the two cyclists? Put both values in the answerbox, separated with a comma, and select the appropriate units.
Answer:
Speed of a= 21 miles/hr
r = Speed of b= 7 miles/hr
Speed of a = 3r
Step-by-step explanation:
The cyclist are 112 miles apart
Time traveled by two = 4 hours
Speed of a = 3 * speed of b
If a cylcles 3 times More than b, then a will cover 3*distance of b
But speed = distance/time
Time = 4hours
Total distance=112
a = 3b
3b + b = 112
4b = 112
b = 112/4
b = 28 miles
a = 3b
a = 3*28
a = 84 Miles
They bought traveled 4 hours
Speed of a = 84miles/4 hours
Speed of a= 21 miles/hr
Speed of b = 28miles/4 hours
Speed of b = 7 miles/hr
Find the 17th term of the arithmetic sequence.
-6, 3, 12, 21, ...
The 17th term is
Answer:
nth term = dn + (a - d) Where d is the difference between the terms, a is the first term and n is the term number.
Step-by-step explanation:
9*17 + (-6- 9)= 138
First find the common difference.
This can be found by subtracting the second term minus the
first term which in this case us 3 - (-6) or 3 + (+6) which is 9.
So we add 9 to reach the next term in this sequence.
Since this sequence isn't too long, continuing adding 9
until you reach the 17th term in this arithmetic sequence.
-6 ⇒ 1st term
3 ⇒ 2nd term
12 ⇒ 3rd term
21 ⇒ 4th term
30 ⇒ 5th term
39 ⇒ 6th term
48 ⇒ 7th term
57 ⇒ 8th term
66 ⇒ 9th term
75 ⇒ 10th term
84 ⇒ 11th term
93 ⇒ 12th term
102 ⇒ 13th term
111 ⇒ 14th term
120 ⇒ 15th term
129 ⇒ 16th term
138 ⇒ 17th term
By manually doing this, we found that our 17th term is 138.
You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37. A random sample of 780 men over the age of 50 found that 206 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim. Test the relevant hypotheses using a 10% level of significance. Give answers to at least 4 decimal places. What are the correct hypotheses?
Answer:
1. Yes, the sample data provides convincing evidence to support the claim that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37
2. The correct hypotheses are;
The null hypothesis is H₀: p ≥ p₀
The alternative hypothesis is Hₐ: p < p₀
Step-by-step explanation:
given
The null hypothesis is H₀: p ≥ p₀ where p₀ = 0.37
The alternative hypothesis is Hₐ: p < p₀
The formula for the z test is presented as follows;
[tex]z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0 (1 - p_0)}{n}}}[/tex]
Where:
[tex]\hat p[/tex] = Sample proportion = 206/780 = 0.264
p₀ = Population proportion = 0.37
n = Sample size = 780
α = Significance level = 10% = 0.01
Plugging in the values, we have;
[tex]z=\dfrac{0.264-0.37}{\sqrt{\dfrac{0.37 (1 - 0.37)}{780}}} = -6.13[/tex]
From the the z relation/computation, we have the p value = 0.000000000451
Since the p value which is 0.000000000451 is less than α, which is 0.01 we reject the null hypothesis and we fail to reject the alternative hypothesis, that is there is sufficient statistical evidence to suggest that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37.
what is the area of a circle with a diameter of 8
Step-by-step explanation:
Radius (R) =diameter /2 =8/2 =4
So area=
[tex]\pir {r}^{2} = \pi {4}^{2} = 50.27[/tex]
Hope this helps..
Find the slope of the line that contains the points named.
R(O, 4), S(5,0)
-4/5
4/5
-5/4
Answer:
[tex] - \frac{4}{5} [/tex]
Step-by-step explanation:
Line is passing through the points R (0, 4), S (5, 0)
[tex]Slope \: of \: RS \\ = \frac{4 - 0}{0 - 5} \\ \\ = \frac{4}{ - 5} \\ \\ = - \frac{4}{5} [/tex]
Type the expression that results from the following series of steps:
Start with t times by 5.
Answer:
t times 5 is t * 5 or 5t.
In Don Javier's milking, milk is collected in two containers, one with a 300-liter capacity and one with 180 liters, if they are filled with 15 and 20-liter jugs. Which of the pitchers exactly fill the containers without milk being left over or missing?
Answer:
Both Pitchers
Step-by-step explanation:
First, we determine how many of each pitcher it would take to fill the 300 liter and 180 liter containers.
300÷15=20 of the 15 liter pitcher
300÷20=15 of the 20 liter pitcher
Similarly
180÷15=12 of the 15 liter pitcher.
180÷20=9 of the 20 liter pitcher.
The two pitchers gives a whole number when their volumes divide the volumes of the containers.
Therefore, the two pitchers exactly fill the containers without milk being left over.
Please answer this correctly I want helping hand people to answer this correctly
Answer:
w = 36
Step-by-step explanation:
You can make a ratio 98 : 84 = 42 : w
[tex]\frac{49}{42}=\frac{42}{w}[/tex]
49w = 1764
w = 36
Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is gbb, then R9gbb)=1. Suppose that the random variable X is defined in terms of R as follows: X=2R^2-4R-2. The values of X are thus:
Complete Question
The complete question is shown on the first uploaded image
Answer:
Value x of X -3 -7 -15
[tex]P_X (x)[/tex] [tex]\frac{1}{2}[/tex] [tex]\frac{3}{8}[/tex] [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
From the question we are told that
The values of X are [tex]X = -3 , -7 , -15[/tex]
The total number of outcomes is n = 8
The probability distribution function of X is evaluated as follow
[tex]p(X = -3 ) = \frac{N_{-3}}{n}[/tex]
Where [tex]N{-3}[/tex] is the number of time X = -3 occurred and from the table the value is [tex]N _{-3} = 4[/tex]
Therefore
[tex]p(X = -3 ) = \frac{4}{8}[/tex]
[tex]p(X = -3 ) = \frac{1}{2}[/tex]
Now
[tex]p(X = -7 ) = \frac{N_{-7}}{n}[/tex]
Where [tex]N_{-7} = 3[/tex] from table
So
[tex]p(X = -7 ) = \frac{3}{8}[/tex]
Also
[tex]p(X = -15 ) = \frac{N_{-15}}{n}[/tex]
[tex]p(X = -15 ) = \frac{1}{8}[/tex]
Activity Question 1 When designing a truss, a truss builder might know the base angle measurement and the length of the tie beam needed. The next step is to compute the height of the king post. Let's take a look at some right triangles to see whether knowing the measure of an acute angle of a right triangle and the length of one of the sides is enough to find the lengths of the other two sides. Part A What is the measure of ∠BAC?
Answer:
36.87°
Step-by-step explanation:
Assume the triangles are as in the diagram below.
∠BAC includes ∠DAE.
The measure of ∠BAE is 36.87°.
Answer:
36.87°
Step-by-step explanation:
i just had this question on edmentum and it was right.
What is the most important difference between an experiment and an observational study? An experiment is conducted in a laboratory and an observational study is conducted outside. An experiment has a treated group and a control group while an observational study does not. In an experiment, the researcher applies a treatment to a randomly assigned group and studies the results, while an observational study just looks at things that have happened without intervention. In an experiment, the researcher studies the effects of medical treatments or other scientific results, while an observational study looks at subjects in the social science arena.
Answer:
In an observational study, we measure or survey members of a sample without trying to affect them. In a controlled experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.
hope it helps :)
mark as brainliest
In an experiment, the researcher applies a treatment to a randomly assigned group and studies the results, while an observational study just looks at things that have happened without intervention.
What is an experiment?An experiment is designed to test the effect of an intervention or treatment on a particular outcome, by comparing the results from a group that receives the intervention to a control group that does not receive the intervention. In this way, the experiment can establish cause-and-effect relationships and determine if the treatment has a significant effect.
On the other hand, an observational study does not involve any manipulation of the independent variable. It simply observes and records the relationship between variables. Observational studies cannot establish cause-and-effect relationships and the results may be subject to confounding variables, which can make it difficult to interpret the findings.
Hence, the correct answer would be an option (C).
Learn more about the experiment here:
https://brainly.com/question/17314369
#SPJ6
I need help with this question
Answer:
A 120 deg
Step-by-step explanation:
The sum of the measures of all angles of a circle is 360 deg.
m<HML + m<LMK + m<KMJ + m<JMH = 360 deg
m<HML = 80 deg
m<LMK = 125 deg
m<KMJ = 35 deg since it's the same measure as the measure of arc KJ.
m<HML + m<LMK + m<KMJ + m<JMH = 360 deg
Now we substitute the values we know.
m<80 deg + m<125 deg + 35 deg + m<JMH = 360 deg
240 deg + m<JMH = 360 deg
m<JMH = 120
A middle school band is selling candy bars and nuts to raise money for a field trip. Each candy bar, b, costs $1.50 and each box of nuts, n, costs $4.00. If they raised $418, what expression shows the portion that came from candy bar sales?
Answer:
1.5b = 418 - 4n (all in dollars)
Step-by-step explanation:
Let b represent the number of candy bars sold and n the number of box of nuts sold.
Given that each;
Candy bar costs $1.50
box of nut $4.00
Amount raised from candy bars = $1.50 × b
Amount raised from box of nut = $4.00 × n
Total amount raised = $418
The equation for the total amount raised is;
1.50 × b + 4.00 × n = 418
1.5b + 4n = 418
The portion that came from candy bars is;
Making 1.5b the subject of formula;
1.5b = 418 - 4n
Ashley mixes two types of soft drinks with different types of concentration: one soft drink has 20% sugar and the other drink has 45% sugar. Each can has 250 milliliters of soda. What is the sugar concentration of the mixed soft drink?
Answer:
Sugar concentration of the mixed soft drink will be 32.5%.
Step-by-step explanation:
Sugar concentration of first drink = 20%
Volume of first soda = 250 ml
Sugar in first soda = 20% of 250 ...... (1)
Sugar concentration of second drink = 45%
Volume of second soda = 250 ml
Sugar in second soda = 45% of 250 ...... (2)
Let [tex]x\%[/tex] be the sugar concentration in resultant mixture.
Volume of mixture = 250 + 250 = 500 ml
Sugar in mixture = [tex]x\%[/tex] of 500 ml ...... (3)
Total sugar concentration (Adding (1) and (2)) and equating it to equation (3):
20% of 250 + 45% of 250 = [tex]x\%[/tex] of 500
[tex]\Rightarrow \dfrac{20}{100} \times 250 + \dfrac{45}{100} \times 250 = \dfrac{x}{100} \times 500\\\Rightarrow 2 \times x = 65\\\Rightarrow x = 32.5\%[/tex]
Hence, Sugar concentration of the mixed soft drink will be 32.5%.
A recent study reported that 28% of shoppers only review one page when searching online for product information. A random sample of 100 shoppers was randomly selected. What is the probability that between 20 and 30 of these shoppers only review one page when searching online?
Answer:
68.29% probability that between 20 and 30 of these shoppers only review one page when searching online
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 100, p = 0.28[/tex]
So
[tex]\mu = E(X) = np = 100*0.28 = 28[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.28*0.72} = 4.49[/tex]
What is the probability that between 20 and 30 of these shoppers only review one page when searching online?
Using continuity correction, this is [tex]P(20 - 0.5 \leq X \leq 30 + 0.5) = P(19.5 \leq X \leq 30.5)[/tex], which is the pvalue of Z when X = 30.5 subtracted by the pvalue of Z when X = 19.5.
X = 30.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30.5 - 28}{4.49}[/tex]
[tex]Z = 0.56[/tex]
[tex]Z = 0.56[/tex] has a pvalue of 0.7123.
X = 19.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19.5 - 28}{4.49}[/tex]
[tex]Z = -1.89[/tex]
[tex]Z = -1.89[/tex] has a pvalue of 0.0294
0.7123 - 0.0294 = 0.6829
68.29% probability that between 20 and 30 of these shoppers only review one page when searching online
Brainliest to best answer!
Understanding proofs can be challenging for many students. What advice would you
give to a student struggling with these concepts?
Answer:
take your time and always ask for help when needed
Step-by-step explanation:
