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 $29.77 per access line per month, with a standard deviation of $2.55. Company A's operating expenses were $29.00 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.)

Answer 1

Answer:-

Given that:-

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 $29.77 per access line per month, with a standard deviation of $2.55. Company A's operating expenses were $29.00 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.

The difference between company A's and overall average = 29.77-29=0.77

So,
we need to find the proportion of companies having difference of less than 0.77 from the mean . This can be found using:

So,

The percentage is 23.58%