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 point)
Responses
97.09%
2.28%
2.91%
97.72%
To find the percentage of customers who have to wait at least 10 minutes, we need to find the z-score corresponding to a wait time of 10 minutes.
The formula to calculate the z-score is:
z = (x - μ) / σ
where:
x = wait time (10 minutes)
μ = population mean (6.4 minutes)
σ = standard deviation (1.9 minutes)
z = (10 - 6.4) / 1.9
z = 3.6 / 1.9
z = 1.89
Looking up the z-score in the Z-table, we can find the corresponding percentage. However, since the z-score is higher than any z-score listed in the table, we can conclude that the percentage of customers who have to wait at least 10 minutes is greater than 97.72%.
Therefore, the correct answer is 97.72%.
is that correct ?
I apologize for the mistake in my previous response. You are correct, and I apologize for the confusion caused.
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 and then find the percentage of values greater than that z-score.
The formula to calculate the z-score is:
z = (x - μ) / σ
where:
x = wait time (10 minutes)
μ = population mean (6.4 minutes)
σ = standard deviation (1.9 minutes)
z = (10 - 6.4) / 1.9
z = 3.6 / 1.9
z ≈ 1.89
Now we will use the z-score to find the percentage of values greater than that z-score. We will look at the z-table or use a calculator to find the percentage. The percentage of values greater than a z-score of 1.89 is 2.28%.
Therefore, the correct answer is 2.28%. I apologize for the earlier incorrect response.