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.

1. The cash operating expenses of the regional phone companies
during the first half of 1994 were distributed about a mean of
$29.84 per access line per month, with a standard deviation of
$2.95. 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.)

%?

2. The cash operating expenses of the regional phone companies
during the first half of 1994 were distributed about a mean of
$29.27 per access line per month, with a standard deviation of
$2.75. Company N's operating expenses were $35.54 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

Solution :

Given that ,

1) mean = = 29.84

standard deviation = = 2.95

P(x < 28) = P[(x - ) / < (28 - 29.84) / 2.95]

= P(z < -0.62 )

Using z table,

= 0.2676

The percentage is = 26.76%

2) mean = = 29.27

standard deviation = = 2.75

P(x > 35.54) = 1 - p( x< 35.54)

=1- p P[(x - ) / < (35.54 - 29.27) / 2.75]

=1- P(z < 2.28)

Using z table,

= 1 - 0.9887

= 0.0113

The percentage is = 1.13%

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