Mathematics, 22.07.2021 19:40 tjmoney8614

A record store owner finds that 20% of customers entering her store make a purchase. One morning 180 people, who can be regarded as a random sample of all customers, enter the store. a. What is the mean of the distribution of the sample proportion of customers making a purchase?
b) What is the variance of the sample proportion?
c) What is the standard error of the sample proportion?
d) What is the probability that the sample proportion is less than 0.15?

Answers: 2

Show answers

Answers

Answer from: wayneh24

a) 0.2

b) 0.0009

c) 0.0298

d) 0.0465 = 4.65% probability that the sample proportion is less than 0.15.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

20% of customers entering her store make a purchase.

This means that p = 0.2

180 people

This means that n = 180

a. What is the mean of the distribution of the sample proportion of customers making a purchase?

By the Central Limit Theorem, $\mu = p = 0.2$ .

b) What is the variance of the sample proportion?

The standard deviation is:

$s = \sqrt{\frac{0.2*0.8}{180}} = 0.0298$

Variance is the square of the standard deviation, so:

s^2 = (0.0298)^2 = 0.0009

c) What is the standard error of the sample proportion?

As found in the previous item, 0.0298.

d) What is the probability that the sample proportion is less than 0.15?

This is the p-value of Z when X = 0.15. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{0.15 - 0.20}{0.0298}$

Z = -1.68

Z = -1.68 has a p-value of 0.0465.

0.0465 = 4.65% probability that the sample proportion is less than 0.15.

Answer from: Quest

3-4

step-by-step explanation:

the answer is 3-4 because both 45 and 60 has a multiple of 15.

45/3=15

60/4=15

therefore the odds against selecting a red is 4-3

Answer from: Quest

its kind of blurry. can you put a clearer pic?

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 17:30

Janet drove 300 miles in 4.5 hours. write an equation to find the rate at which she was traveling

Answers: 2

Answer

Mathematics, 21.06.2019 17:30

Find the pattern and use it to list the nth term in the sequence. 6, 12, 20, 30, 42, 56, the nth term of the sequence is

Answers: 3

Answer

Mathematics, 21.06.2019 20:30

Twelve less than a number is at most 20

Answers: 1

Answer

Mathematics, 21.06.2019 21:40

Write the contrapositive of the conditional statement. determine whether the contrapositive is true or false. if it is false, find a counterexample. a converse statement is formed by exchanging the hypothesis and conclusion of the conditional. a) a non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. true b) a statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. false; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional. c) a non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. false; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional. d) a statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. true

Answers: 1

Answer

You know the right answer?

A record store owner finds that 20% of customers entering her store make a purchase. One morning 180...

Questions