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.

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 and standard deviation , the zscore of a measure X is given by:

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 and standard deviation , a large sample size, of at least 30, can be approximated to a normal distribution with mean and standard deviation

In this problem, we have that:

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

By the Central Limit Theorem

has a pvalue of 0.9812

X = 76

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: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.