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.(
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.