Question

1. 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.

A) The cash operating expenses of the regional phone companies during the first half of 1994 were distributed about a mean of $29.94 per access line per month, with a standard deviation of $2.45. 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.)

B) The cash operating expenses of the regional phone companies during the first half of 1994 were distributed about a mean of $29.16 per access line per month, with a standard deviation of $2.15. Company N's operating expenses were $35.60 per access line per month in the first half of 1994. Estimate the percentage of regional phone companies whose operating expenses were higher than those of Company N. (Round your answer to two decimal places.)

Answer 1

1.

A) Given that:

Company A's operating expenses = $28.00

X= 28

Corresponding z score is ,

To estimate the percentage of regional phone companies whose operating expenses were closer to the mean.

The required probability is ,

P(-0.79<z<0.79)

=P(z < 0.79) - P(z<-0.79)

Using Excel function = NORMSDIST (z)

=0.7852 - 0.2148

=0.5704

= 57.04%

Therefore 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 is 57.04%

B)

Given that:

Company N's operating expenses = $35.60

X=35.60

Required probability is P(X>35.60)

P(z>3)=1-P(z<3)

Using Excel function = NORMSDIST (z)

= 1-0.9987

=0.0013

=0.13%

Therefore the percentage of regional phone companies whose operating expenses were higher than those of Company N is 0.13%