Question

The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes. how long do the longest 10% of calls last?

Answer 1

To solve this problem, we use the formula:

z = (x – u) / s

where z is the z score value which can be obtained from the tables, x is the sample value, u is the mean = 6.3 min, and s is the std dev = 2.2 min

 

at P value = 0.90, the z = 1.28, finding for x:

x = z s + u

x = 1.28 * 2.2 + 6.3

x = 9.116

 

at P value = 1.0, the z = 3.49, finding for x:

x = z s + u

x = 3.49 * 2.2 + 6.3

x = 13.978 ~ 14

 

Therefore the longest 10% calls last about 9.1 minutes to 14 minutes