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 $29.9 per access line per month, with a standard deviation of $2.45. Company N's operating expenses were $37.03 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

Let X be the random variable denoting the cash operating expenses of the regional phone companies during the first half of 1994 (in $).

Thus, X ~ N(29.9, 2.45) i.e. (X - 29.9)/2.45 ~ N(0,1)

The probability of regional phone companies whose operating expenses were higher than those of Company N = P(X > 37.03) = 1 - P(X 37.03) = 1 - P[(X - 29.9)/2.45 (37.03 - 29.9)/2.45] = 1- P[(X - 29.9)/2.45 2.9102) = 1 - (2.9102) = 1 - 0.9982 = 0.0918

[(.) is the cdf of N(0,1)]

Hence, the required percentage is 9.18%.

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