A small hair salon in Denver, Colorado, averages about 82 customers on weekdays

Question

A small hair salon in Denver, Colorado, averages about 82 customers on weekdays with a standard deviation of 16. 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 $4 discount on 7 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 7 weekday period jumps to 93. Use Table 1. a. What is the probability to get a sample average of 93 or more customers if the manager had not offered the discount? (Round intermediate calculations to 4 decimal places, "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? No, there is good chance (more than 5%) of getting 93 or more customers without the discount. No, there is only a small chance (less than 5%) of getting 93 or more customers without the discount. Yes, there is good chance (more than 5%) of getting 93 or more customers without the discount. Yes, there is only a small chance (less than 5%) of getting 93 or more customers without the discount.

Explanation / Answer

Probability to get a sample average of 93 or more when no discounts

For x = 93, z = (93 - 82) / 16 = 0.6875

Hence P(x > 93) = P(z > 0.6875) = [total area] - [area to the left of 0.6875]

= 1 - 0.7541 = 0.2459

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