A key metric in the cell phone industry is average revenue per user (ARPU), which represents the average dollar amount that a customer spends per store visit. In 2011, AT&T reported their ARPU as $63.76. Suppose the standard deviation for this population is $22.50. What is the probability that the ARPU will be between $60 and $63 from a random sample of 38 customers?
A) 0.5517
B) 0.4168
C) 0.2661
D) 0.1515

Question

Quizplus · Accepted Answer

We need to use the formula for calculating the z-score, which is (x̄ - μ) / (σ / √n), where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

For the lower limit of $60: 
z = (60 - 63.76) / (22.50 / √38) = -1.67

For the upper limit of $63: 
z = (63 - 63.76) / (22.50 / √38) = -0.28

We can then use a z-table or calculator to find the probability that the z-score falls between -1.67 and -0.28, which is 0.2661. Therefore, the answer is C.

A Key Metric in the Cell Phone Industry Is Average