A bank offers customer service through the telephone. The wait time for customers before speaking to a representative on the telephone line during peak hours is normally distributed with a population mean of 6.4 minutes and a standard deviation of 1.9 minutes. What percentage of customers using the telephone service line have to wait at least 10

minutes? Round to two decimal places.(

1 answer

To find the percentage of customers who have to wait at least 10 minutes, we need to calculate the z-score for a wait time of 10 minutes.

The formula for calculating the z-score is:

z = (X - µ) / σ

Where X is the wait time, µ is the population mean, and σ is the standard deviation.

In this case, X = 10 minutes, µ = 6.4 minutes, and σ = 1.9 minutes.

z = (10 - 6.4) / 1.9
z = 3.6 / 1.9
z = 1.89

Next, we need to find the proportion of the normal distribution that is less than or equal to this z-score.

Using a standard normal distribution table or calculator, we can find that the proportion to the left of a z-score of 1.89 is approximately 0.9706.

To find the proportion of customers who have to wait at least 10 minutes, we subtract this proportion from 1:

1 - 0.9706 = 0.0294

Therefore, approximately 2.94% of customers using the telephone service line have to wait at least 10 minutes.