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The cash operating expenses of the regional phone companies during the first half of 1994 were distributed about a mean of $29.93 per access line per month, with a standard deviation of $2.65. Company A's operating expenses were $27.00 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.)

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Answer:

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 73%.

Step-by-step explanation:

The Company A's operating expenses were $27.00. This is $2.93 less than the regional mean.

[tex]\Delta E=29.93-27.00=2.93[/tex]

The companies whose operating expenses are closer to the mean are the ones that have expenses $2.93 below or above the mean.

The fraction of companies that are closer to the mean is equal to the proability of having expenses between those two limits:

[tex]z_1=(M-\mu)/\sigma=-2.93/2.65=-1.105\\\\z_2=+1.105[/tex]

[tex]P(|z|\leq1.105)=P(z\leq 1.105)-P(z<-1.105)=0.86542-0.13458=0.73[/tex]

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