This exercise uses the normal probability density function and requires the use

Question

This exercise uses the normal probability density function and requires the use of either technology or a table of values of the standard normal distribution. The cash operating expenses of the regional phone companies during the first half of 1994 were distributed about a mean of $29.79 per access line per month, with a standard deviation of $2.35. Company A's operating expenses were $28.00 per access line per month. Assuming a normal distribution of operating expenses, estimate the percentage of regional phone companies whose operating expenses were closer to the mean than the operating expenses of Company A were to the mean. (Round your answer to two decimal places.)

Explanation / Answer

Solution:

We are given

Population mean = 29.79

Population standard deviation = 2.35

Sample mean = 28

We have to find P(X<28)

The z score formula is given as below:

Z = (sample mean – population mean) / population standard deviation

Z = (28 – 29.79) / 2.35

Z = -0.7617

P(Z<-0.7617) = 0.223119   by using z-table or excel

P(X<28) = P(Z<-0.7617) = 0.223119

Required percentage = 22.31%

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