Question
In: Statistics and Probability
This exercise uses the normal probability density function and requires the use of either technology or...
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.)
Solutions
Expert Solution
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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orchestra answered 2 years agoRelated Solutions
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