The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. Based on this, what is the probability that a call will last longer than 13 minutes?
A) About 0.0125
B) Approximately 0.4875
C) About 0.5125
D) About 0.9875

Question

Quizplus · Accepted Answer

To find the probability that a call will last longer than 13 minutes, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest (13 minutes), μ is the mean (8.21 minutes), and σ is the standard deviation (2.14 minutes). Plugging in the values, we get Z = (13 - 8.21) / 2.14 ≈ 2.24. Looking up the Z-score of 2.24 in a standard normal distribution table or using a calculator, we find that the area to the left of Z is approximately 0.9875, meaning the area to the right (the probability of a call lasting longer than 13 minutes) is 1 - 0.9875 = 0.0125.

The Manager of a Computer Help Desk Operation Has Collected