Question

Assume the hold time of callers to a cable company is normally distributed with a mean of 5.3 minutes and a standard deviation of 0.6 minute. Determine the percent of callers who are on hold between 4.5 minutes and 5.5 minutes.

a) 15.87%
b) 30.85%
c) 9.12%
d) 58.72%

Answer 1

To find the percent of callers on hold between 4.5 minutes and 5.5 minutes, we need to calculate the area under the normal distribution curve between those two values. By calculating the Z-scores corresponding to 4.5 minutes and 5.5 minutes and finding the area between those Z-scores, we can determine the percentage. The correct answer is b) 30.85%.

Step-by-step explanation:

To determine the percent of callers who are on hold between 4.5 minutes and 5.5 minutes, we need to calculate the area under the normal distribution curve between those two values. The Z-score formula is used to find the area under the curve corresponding to a specific range of values. Z = (X - μ) / σ, where X is the specific value, μ is the mean, and σ is the standard deviation. We need to find the Z-scores for 4.5 minutes and 5.5 minutes using the given mean and standard deviation.

Z1 = (4.5 - 5.3) / 0.6 = -0.8
Z2 = (5.5 - 5.3) / 0.6 = 0.33

Using Z-tables or a calculator, we can find the area to the left of Z1 and Z2. The area between Z1 and Z2 represents the percentage of callers who are on hold between 4.5 minutes and 5.5 minutes. The area between -0.8 and 0.33 is approximately 30.85%. Therefore, the correct answer is b) 30.85%.