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 $29.98 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

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 29.98
standard Deviation ( sd )= 2.35

Company A's operating expenses were $28.00 per access line per month
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
P(X < 28) = (28-29.98)/2.35
= -1.98/2.35= -0.84
= P ( Z <-0.84) From Standard Normal Table
= 0.2
= 20%

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