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 “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability =

b. Do you feel confident that the manager’s discount strategy has worked? No, there is good chance (more than 5%) of getting 79 or more customers without the discount. No, there is only a small chance (less 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. Yes, there is only a small chance (less than 5%) of getting 79 or more customers without the discount.

Explanation / Answer

a) P(X > 79)

   = P((X - mean)/sd > (79 - mean)/sd)

= P(Z > (79 - 72)/11)

= P(Z > 0.64)

= 1 - P(Z < 0.64)

= 1 - 0.7389

= 0.2611

b) Yes, there is good chance (more than 5% ) of getting 79 or more customers without discount

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