A small hair salon in Denver, Colorado, averages about 72 customers on weekdays

Question

A small hair salon in Denver, Colorado, averages about 72 customers on weekdays with a standard deviation of 11. 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 $5 discount on 9 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 9 weekday period jumps to 79. Use Table 1. a. What is the probability to get a sample average of 79 or more customers if the manager had not offered the discount? (Round your intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability _____ b. Do you feel confident that the managers discount strategy has worked? No, there is only a small chance (less than 5%) of getting 79 or more customers without the discount. Yes, there is only a small chance (less than 5%) of getting 79 or more customers without the discount. No, there is good chance (more than 5%) of getting 79 or more customers without the discount. Yes, there is good chance (more than 5%)of getting 79 or more customers without the discount.

Explanation / Answer

(a)

Calculating z-score as follows:

z = (79-72)/11 = 0.636

Using a z-table to calculate the cumulative probability for a single tailed test, we get:

p = 0.737

So, required probability = 1-p = 1-0.737 = 0.263

(b)

The critical z-score for the one tailed test at significance level of 5% is 1.64.

Since 0.636<1.64, So, answer iss:

NO, there is only a small chance ( less than 5% ) that the manager's strategy has worked.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.