Question

1. 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 $29.97 per
access line per month, with a standard deviation of $2.25. 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. 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 $29.79 per
access line per month, with a standard deviation of $2.85. Company
N's operating expenses were $38.29 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 :

1) Given that ,

mean = = 29.97

standard deviation = = 2.25

P(x < 28) = P[(x - ) / < (28 - 29.97) /2.25 ]

= P(z < -0.88)

Using z table,

= 0.1894

The percentage is = 18.94%

2) Given that ,

mean = = 29.79

standard deviation = = 2.85

P(x > 38.29) = 1 - p( x< 38.29)

=1- p P[(x - ) / < (38.29 - 29.79) /2.85 ]

=1- P(z < 2.98)

Using z table,

= 1 - 0.9986

= 0.0004

The percentage is = 0.04%

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