A small hair salon in Denver, Colorado, averages about 30 customers on weekdays with a standard deviation of 6. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $2 discount on 5 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 5 weekday period jumps to 35. Required:
What is the probability to get a sample average of 35 or more customers if the manager had not offered the discount?

0.0314 = 3.14% probability to get a sample average of 35 or more customers if the manager had not offered the discount

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 and standard deviation , the z-score 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 p-value, 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 and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

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

A small hair salon in Denver, Colorado, averages about 30 customers on weekdays with a standard deviation of 6.

This means that

5 consecutive weekdays.

This means that

What is the probability to get a sample average of 35 or more customers if the manager had not offered the discount?

This is 1 subtracted by the pvalue of Z when X = 35.

By the Central Limit Theorem

has a pvalue of 0.9686

1 - 0.9686 = 0.0314

0.0314 = 3.14% probability to get a sample average of 35 or more customers if the manager had not offered the discount

your question is incomplete, write all the numbers in the sequence that it tells you.  

step-by-step explanation:

answer: 72: 111

step-by-step explanation: