Answer:
a) 34.46% probability that her pulse rate is greater than 70 beats per minute.
b) 2.28% probability that they have pulse rates with a mean greater than 70 beats per minute.
c) Because the underlying distribution(female's pulse rate) is normal.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Distribution of females pulse rates:
Here, i suppose there was a typing mistake, since the mean and the standard deviation are lacking.
Also, the question c. only makes sense if the distribution is normal, so i will treat it as being.
I will use [tex]\mu = 68, \sigma = 5[/tex]. I am guessing these values, just using them to explain the question.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is greater than 70 beats per minute.
This is 1 subtracted by the pvalue of Z when X = 70. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 68}{5}[/tex]
[tex]Z = 0.4[/tex]
[tex]Z = 0.4[/tex] has a pvalue of 0.6554
1 - 0.6554 = 0.3446
34.46% probability that her pulse rate is greater than 70 beats per minute.
b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean greater than 70 beats per minute.
Now [tex]n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 70. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{70 - 68}{1}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
1 - 0.9772 = 0.0228
2.28% probability that they have pulse rates with a mean greater than 70 beats per minute.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30
The sample size only has to exceed 30 if the underlying distribution is normal. Here, the distribution of females' pulse rate is normal, so this requirement does not apply.
Which statement about the temperatures −13.4°C and −13.2°C is true?
-13.4°C>−13.2°C because −13.2°C is older than −13.4°C.
−13.4°C<−13.2°C because −13.2°C is colder than −13.4°C.
−13.4°C<−13.2°C because −13.2°C is warmer than −13.4°C.
−13.4°C>−13.2°C because −13.2°C is warmer than −13.4°C.
Answer:
I think "−13.4°C<−13.2°C because −13.2°C is warmer than −13.4°C" is the right answer
Which number produces a rational number when multiplied by 0.5
Answer:
Step-by-step explanation:B is a rational number and therefore when added to 0.5 produces another rational number, 0.75.
A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were: At the .02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Determine the p-value.
Answer:
We conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.
Step-by-step explanation:
The complete question is: A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were:
Number sampled: 1,000 (republican) , 800 (democrats)
Number in favor: 200 (republican) , 168 (democrats)
At the 0.02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Determine the p-value.
Let [tex]p_1[/tex] = proportion of Republicans in favor of lowering the standards.
[tex]p_2[/tex] = proportion of Democrats in favor of lowering the standards.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1 \geq p_2[/tex] {means that there is an equal or larger proportion of Republicans in favor of lowering the standards}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1 < p_2[/tex] {means that there is a larger proportion of Democrats in favor of lowering the standards}
The test statistics that would be used here Two-sample z-test for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of Republicans in favor of lowering the standards = [tex]\frac{200}{1000}[/tex] = 0.20
[tex]\hat p_2[/tex] = sample proportion of Democrats in favor of lowering the standards = [tex]\frac{168}{800}[/tex] = 0.21
[tex]n_1[/tex] = sample of Republicans = 1000
[tex]n_2[/tex] = sample of Democrats = 800
So, the test statistics = [tex]\frac{(0.20-0.21)-(0)}{\sqrt{\frac{0.20(1-0.20)}{1000}+\frac{0.21(1-0.21)}{800} } }[/tex]
= -0.52
The value of z test statistics is -0.52.
Now, P-value of the test statistics is given by the following formula;
P-value = P(Z < -0.52) = 1 - P(Z [tex]\leq[/tex] 0.52)
= 1 - 0.6985 = 0.3015
Now, at 0.02 significance level, the z table gives a critical value of -2.054 for left-tailed test.
Since our test statistic is more than the critical value of z as -0.52 > -2.054, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.
The three hands of an accurate 12-hour clock make a total of _?_ complete revolutions around the clock’s face every 24 hours. (A) 72 (B) 733 (C) 1466 (D) 10 104
Answer:
(C) 1466
Step-by-step explanation:
The hour hand makes one revolution each 12 hours. So it makes 2 revolutions a day.
The minute hand makes one revolution each hour. So it makes 24 revoulutions a day.
The second hand makes one revolution each minute. So it makes 24*60 = 1440 revolutions a day.
In total:
2 + 24 + 1440 = 1466
The correct answer is C.
Help people like mE out
Solution,
radius=10 cm
Circumference of circle=2 pi r
=2*3.142*10
=62.84 cm
hope it helps
Good luck on your assignment
What’s the correct answer for this?
Answer:
20
Step-by-step explanation:
Since chord AB and DE are at equal length from the centre, they are equal in length.
AB = DE
3x-7 = 5(x-5)
3x-7 = 5x-25
-7+25 = 5x -3x
18 = 2x
Dividing both side by 2
x = 9
Now
AB = 3(9)-7
= 27 -7
= 20
A 12-centimeter rod is held between a flashlight and a wall as shown. Find the length of the shadow on
the wall of the rod is 45 cm from the wall and 15 cm from the light.
Answer:
48 cm
Step-by-step explanation:
Given:
Distance of rod from the wall = 45 cm
Distance of rod from the light = 15 cm
Length of rod = 12 cm
We can see that <DAM and <BAF are equal
Also, <DMA and <BFM are equal because they are corresponding angles
To find the length of the shadow, let's take the equation
[tex] \frac{DM}{BF} = \frac{AM}{A.F} [/tex]
Where.:
DM = ½ of length of the rod = ½*12 = 6
A.F = 15 + 45 = 60 cm
AM = 15 cm
Therefore,
[tex] \frac{DM}{BF} = \frac{AM}{A.F} [/tex]
[tex]= \frac{6}{BF} = \frac{15}{60} [/tex]
Cross multiplying, we have:
15 * B.F = 60 * 6
15 * B.F = 360
[tex]BF = \frac{360}{15}[/tex]
BF = 24 cm
The shadow on the wall =
2 * BF
= 2 * 24
= 48 cm
The shadow on the wall is 48 cm
You borrow $A at an interest rate of r% (per month) and pay it off over t months by making monthly payments of P = g(A, r, t) dollars. Suppose you plan to borrow $ 4000 with a monthly interest rate of 2 % for 12 months. In financial terms, what do the following statements tell you?
a. gA (8000, 2, 12) = 0.045
b. gr (8000, 2, 12) = 44.79
2. Lupe put $11,500 in a certificate of deposit that gained simple interest at a rate of 6.7%. How much interest
did the account gain after 5 months?
Answer:
321
Step-by-step explanation:
Principal amount = $11,500
Simple interest = 6.7%
time :5 months
as simple interest is calculated for a year, time needs to be calculated in years
12 months comprises 1 year
1 month is equivalent to 1/12 years
thus, 5 month is equivalent to (1/12)* 5 years
time in years = 5/12
Simple interest is calculated by formula
SI = p*r*t/100
where SI is simple interest earned
p is principle amount
r is rate of interest
t is time in years
substituting the value of p, r and t in the formula for SI, we have
SI = (11500*6.7*5)\12*100 = 321.04
interest,the account gained after 5 months is 321.
The sum of three consecutive natural numbers is 939, find the numbers. The three numbers in increasing order are _______, ________, and _________
Answer:
312, 313, and 314
Step-by-step explanation:
Since the three numbers are consecutive, each one is one larger than the last. Therefore, we can express them as x, (x+1), and (x+2). Therefore:
[tex]x+(x+1)+(x+2)=939 \\\\3x+3=939 \\\\3x=936\\\\x=312\\\\x+1=313\\\\x+2=314[/tex]
Hope this helps!
How long would it take Belinda's $800 investment to double in value if she has a bond with a 8.75% interest rate?
Answer:
it takes approximately 11 years and 3 months (11.4 years) for Belinda's investments to double.
Step-by-step explanation:
To calculate the time it takes for Belinda's money to double, we will use the simple interest formula as shown below:
Simple interest = P × R × T
where:
P = principal = $800
R = Rate in decimal = 8.75% = 0.0875
T = time = ???
simple interest = $800 ( her money doubles)
∴ 800 = 800 × 0.0875 × t
800 = 70 × t
∴ t = 800 ÷ 70 = 11.4 years. (11 years and 3 months)
Therefore after approximately 11 years and 3 months, Belinda's investments doubles
Answer:
8.23
how long would it take belinda's $800 investment to double in value if she has a bond with a 8.75% interest rate?
A phone company charges $0.45 for the first minute and $0.35 for each additional minute for a long distance call. Which numerical expression can be used to find the cost of a 20-minute phone call? How much does the 20-minute phone call cost?HURRY FIRST ONE GETS BRAINLIEST
Answer:
$0.45+19*$0.35= $7.1
Step-by-step explanation:
first minute= $0.45
subsequent minutes= $0.35
cost per 20 min= $0.45+19*$0.35= $7.1
cost per x min= 0.45+(x-1)*0.35= 0.35x +0.10
Answer:
Step-by✔ 0.45 + 0.35(19)
✔ $7.10
The sum of two numbers is 82. One number is 38 more than the other. Find the numbers.
Answer: 22, 60
Step-by-step explanation:
x+ x + 38 = 82
2x + 38 = 82
2x = 82 - 38
x = 44 / 2 = 22
Answer: 22, 60
Step-by-step explanation:
We can use system of equations to solve this. Let's use 1 for one number and y for the second number.
Equation 1
x+y=82
Equation 2
x+38=y
Since we know what y is, we can substitute it into the first equation.
x+(x+38)=82
x+x+38=82
2x+38=82
2x=44
x=22
Now that we know x, we cna plug it into any equaiton to find y.
(22)+38=y
y=60
What is 1/3 divided by 3
Answer:
1/9 or 0.11
Step-by-step explanation:
1/3 divided by 3
= 1/3 / 3
= 1/3 / 3/1
= 1/3 x 1/3 (the rule is a/b / c/d = a/b * d/c)
= 1/9 or 0.11(1 continues repeating for ever so just make it 0.11)
Plssss answerrr the question is ez
Answer:
yes, the birdhouse has a surface area of 210 inches while the plywood has 1152 inches of surface area
yes the birdhouse is 210 inches while the wood is 1152
A study done by researchers at a university concluded that 70 70% of all student athletes in this country have been subjected to some form of hazing. The study is based on responses from 1 comma 900 1,900 athletes. What are the margin of error and 95% confidence interval for the study? The margin of error is nothing .
Answer:
The margin of error is 0.0206 = 2.06 percentage points.
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.6794, 0.7206).
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].
For this problem, we have that:
[tex]n = 1900, \pi = 0.7[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.7*0.3}{1900}} = 0.0206[/tex]
The margin of error is 0.0206 = 2.06 percentage points.
The lower limit of this interval is:
[tex]\pi - M = 0.7 - 0.0206 = 0.6794[/tex]
The upper limit of this interval is:
[tex]\pi + M = 0.7 + 0.0206 = 0.7206[/tex]
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.6794, 0.7206).
Question 4
Evelyn packed this box with 1-inch cubes. Which expression does NOT
show how Evelyn can find the volume of the box?
6 x 6
2 x 3 x 6
height
2 + 3 + 6
6 + 6 + 6 + 6 + 6 + 6
width
length
Answer:
432
Step-by-step explanation:
Volume is equal to the length*width*height that is 6*6*2*3*6(basically multiply them all in simple terms)=432
Answer:
2 + 3+ 6
Step-by-step explanation:
You are supposed to multiply the length, width, and height not add it.
Which of these leaders would most likely have
spoken these words?
Tecumseh
Thomas Jefferson
Andrew Jackson
Answer:andrew Jackson
Answer:
D
Step-by-step explanation:
thank the person above ☝☝☝
Edge 2021
Rounded to three decimal places, the value of the irrational number e is?
Answer:
2.178
hope it helps!
Answer:
2.718
______________________________
help asap !! will get branliest.
Answer:
0.8
Step-by-step explanation:
(2 x 10^-4)
= 0.0002
(4x10^3)
= 4000
0.0002 x 4000 = 0.8
What is the index when x^2/3 is rewritten as a radical expression?
Answer:
Step-by-step explanation:
[tex]\sqrt[3]{x^{2} }[/tex] written as a radical expression
The radical is the symbol that is used to represent the root in the expression n√x. The index in the given expression x^(2/3) when rewritten as a radical expression is 3.
What is a radical?The radical is the symbol that is used to represent the root in the expression n√x.
Given the expression [tex]x^{\frac23}[/tex], which can be rewritten in the form of radical as,
[tex]x^{\frac23}\\\\[/tex]
[tex]= x^{2 \times \frac13}\\\\[/tex]
Using the law of exponent, [tex]a^{\frac1x} = \sqrt[x]{a}[/tex], then we can write,
[tex]= \sqrt[3]{x^2}[/tex]
Now, in the given expression 3 is an index, x² is the radicand and the symbol √ is known as the radical.
Hence, the index in the given expression x^(2/3) when rewritten as a radical expression is 3.
Learn more about the Radical here:
https://brainly.com/question/1369233
#SPJ2
the ratio of bicycles to to cars is 2:7 respectively. If the total number of vehicles are 63, how many bicycles are there?
Answer:
49 cars and 14 bikes
Step-by-step explanation:
we know [tex]7^{2}[/tex] is 49. 7 × 7 = 49
to match that, 7 × 2 = 14
14 plus 49 is 63
The lengths of pregnancies in a small rural village are normally distributed with a mean of 262 days and a standard deviation of 17 days.In what range would you expect to find the middle 68% of most pregnancies
Answer:
The range in which we can expect to find the middle 68% of most pregnancies is [245 days , 279 days].
Step-by-step explanation:
We are given that the lengths of pregnancies in a small rural village are normally distributed with a mean of 262 days and a standard deviation of 17 days.
Let X = lengths of pregnancies in a small rural village
SO, X ~ Normal([tex]\mu=262,\sigma^{2} = 17^{2}[/tex])
Here, [tex]\mu[/tex] = population mean = 262 days
[tex]\sigma[/tex] = standard deviation = 17 days
Now, the 68-95-99.7 rule states that;
68% of the data values lies within one standard deviation points.95% of the data values lies within two standard deviation points.99.7% of the data values lies within three standard deviation points.So, middle 68% of most pregnancies is represented through the range of within one standard deviation points, that is;
[ [tex]\mu -\sigma[/tex] , [tex]\mu + \sigma[/tex] ] = [262 - 17 , 262 + 17]
= [245 days , 279 days]
Hence, the range in which we can expect to find the middle 68% of most pregnancies is [245 days , 279 days].
WILL GIVE BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST AND CORRECT
Answer:
Step-by-step explanation:
1. 30 plants
the rest were confusing sorry
Please help! Correct answer only, please! Consider the matrix shown below: Find the determinant of the matrix C. Group of answer choices A. -14 B. 14 C. -22 D. The determinant cannot be found for a matrix with these dimensions.
Answer:
Hello There Again. The correct answer 14.
Explanation: Because you need to do Multpliy 2 and 4 and then add again 8 and 6 to get 14 2x4=8+6=14.
Hope It Helps! :)
Answer:
Well, I think the the right answer is 14. Because, 2 x 8 + 6 - 4 - 5 + 1= 14
Hope This Helps!!~
Good Luck!~
With a cupon you can buy up to 6 medium pizzas at 8$ each. What is the domain of this graph ?
Answer:
x=1, 2, 3, 4, 5, 6
Step-by-step explanation:
Let's use logic. You can not have negative pizzas, and I assume you can not have decimals of pizzas.
That means that with the coupon you can only buy whole pizzas up to 6.
So the domain or x is1, 2, 3, 4, 5, 6
Y is directly proportional to the square root of p h=5.4 when p=1.44 find h when p= 2.89
Answer:
I dont know what the answer is exactly
In a cookie jar, 1/5 of the cookies are chocolate chip and 1/2 or the rest a peanut butter. What fraction of all the cookies is peanut butter?
Answer:
If 1/5 are chocolate chip, then 4/5 are not chocolate chip because 1 - 1/5 = 4/5. Half of 4/5 are peanut butter. Half of 4/5 is 2/5, so 2/5 of the cookies are peanut butter.
hope it helps!!!!! :]
The circle is centered at the origin and the length of its radius is three. What is the circles equation
Answer:
x^2 + y^2 = 3^2
Step-by-step explanation:
Use the standard equation of a circle with center at (h, k) and radius r:
(x - 0)^2 + (y - k)^2 = 3^2, or
x^2 + y^2 = 3^2
A Poker club has 10 members. A president and a vice-president are to be selected. In how many ways can this be done if everyone is eligible?
Answer:
90 different ways
Step-by-step explanation:
We have a total of 10 members, and we want to find how many groups of 2 members we can have, where the order of each member in the group of 2 is important, so we have a permutation problem.
To solve this problem, we need to calculate a permutation of 10 choose 2.
The formula for a permutation of n choose p is:
[tex]P(n, p) = n! / (n - p)![/tex]
So we have:
[tex]P(10, 2) = 10! / (10 - 2)![/tex]
[tex]P(10, 2) = 10! / 8![/tex]
[tex]P(10, 2) = 10*9 = 90[/tex]
So there are 90 different ways of choosing a president and a vice-president.
