Question

These exercises use 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 $29.78 per access line per month, with a standard deviation of $2.15. 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.)

b. Repeated measurements of a student's IQ yield a mean of 100, with a standard deviation of 10. What is the probability that the student has an IQ between 96 and 104? (Round your answer to four decimal places.)

Answer 1

a:

Difference between mean and company A expenses is

$29.78 - $29.00 = $0.78

The company operating expenses were closer to the mean than the operating expenses of Company A if company expenses are greater than $29.00 and less than $29.78 + $0.78 = $30.56. That is distance form mean to either side of mean is less than $0.78.

Answer: 28.12%

(b)

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