Mathematics, 21.02.2020 20:27 jdchacon117

According to the latest financial reports from a sporting goods store, the mean sales per customer was $75 with a population standard deviation of $6. The store manager believes 39 randomly selected customers spent more per transaction. What is the probability that the sample mean of sales per customer is between $76 and $77 dollars? You may use a calculator or the portion of the z -table given below. Round your answer to two decimal places if necessary.

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Answer from: lailahussain99

13.04% probability that the sample mean of sales per customer is between $76 and $77 dollars.

Step-by-step explanation:

To solve this problem, we have to understand the Normal Probability Distribution and the Central Limit Theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size, of at least 30, can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 75, \sigma = 6, n = 39, s = \frac{6}{\sqrt{39}} = 0.96$

What is the probability that the sample mean of sales per customer is between $76 and $77 dollars?

This is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 76. So

X = 77

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

By the Central Limit Theorem

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

$Z = \frac{77 - 75}{0.96}$

Z = 2.08

Z = 2.08 has a pvalue of 0.9812

X = 76

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

$Z = \frac{76 - 75}{0.96}$

Z = 1.04

Z = 1.04 has a pvalue of 0.8508

0.9812 - 0.8508 = 0.1304

13.04% probability that the sample mean of sales per customer is between $76 and $77 dollars.

Answer from: Quest

-8

step-by-step explanation:

Answer from: Quest

definition: a circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. we use the symbol ⊙ to represent a circle. the a line segment from the center of the circle to any point on the circle is a radius of the circle.

step-by-step explanation:

i googled it and this is what i got i don't know how it is. sorry.

The set of all points in a plane that are equidistant from two points is a(n): a. line b. point

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