# A small hair salon in Denver, Colorado, averages about 23 customers on weekdays with a standard...

## Question:

A small hair salon in Denver, Colorado, averages about 23 customers on weekdays with a standard deviation of 4. 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 $3 discount on 4 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 4 weekday period jumps to 27. Use Table 1.

a. What is the probability to get a sample average of 27 or more customers if the manager had not offered the discount? (Round ?z? value to 2 decimal places, and final answer to 4 decimal places.)

b. Do you feel confident that the manager?s discount strategy has worked?

1. No, there is good chance (more than 5%) of getting 27 or more customers without the discount.

2. No, there is only a small chance (less than 5%) of getting 27 or more customers without the discount.

3. Yes, there is good chance (more than 5%) of getting 27 or more customers without the discount.

4. Yes, there is only a small chance (less than 5%) of getting 27 or more customers without the discount.

## Probability Under Normal Distribution:

Standard normal distribution is most common and widely used type of continuous distribution with a mean of zero and standard deviation of one. For example, weight, measurement errors and IQ scores follows normal distribution. Most observations are clustered around the mean giving a bell-shaped curve.

## Answer and Explanation:

**a).**

Given that;

{eq}X\sim N(23, 4)\\P(\bar x>27)=? {/eq}

Use z score formula for the sample to find z value that correspond to sample mean of 27...

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#### Learn more about this topic:

from Statistics 101: Principles of Statistics

Chapter 6 / Lesson 9