Probability Calculation Using Normal Distribution and Z
score
88. Refer to the Baseball 2005 data, which reports
information on the 30 major league teams for the 2005 baseball season.
1. Select
the variable team salary and find the mean, median, and the standard deviation.
2. Select
the variable that refers to the age the stadium was built. (Hint: Subtract the
year in which the stadium was built from the current year to find the stadium
age and work with that variable.) Find the mean, median, and the standard
deviation.
56. Assume the likelihood that any flight on Northwest
Airlines arrives within 15 minutes of the scheduled time is .90. We select four
flights from yesterday for study.
1. What is
the likelihood all four of the selected flights arrived within 15 minutes of
the scheduled time?
2. What is
the likelihood that none of the selected flights arrived within 15 minutes of
the scheduled time?
3. What is
the likelihood at least one of the selected flights did not arrive within 15
minutes of the scheduled time?
64. An internal study by the Technology Services department
at Lahey Electronics revealed company employees receive an average of two
emails per hour. Assume the arrival of these emails is approximated by the
Poisson distribution.
1. What is
the probability Linda Lahey, company president, received exactly 1 email
between 4 P.M. and 5 P.M. yesterday?
2. What is
the probability she received 5 or more email during the same period?
3. What is
the probability she did not receive any email during the period?
50. Fast Service Truck Lines uses the Ford Super Duty F-750
exclusively. Management made a study of the maintenance costs and determined
the number of miles traveled during the year followed the normal distribution.
The mean of the distribution was 60,000 miles and the standard deviation 2,000
miles.
1. What
percent of the Ford Super Duty F-750s logged 65,200 miles or more?
2. What
percent of the trucks logged more than 57,060 but less than 58,280 miles?
3. What
percent of the Fords traveled 62,000 miles or less during the year?
4. Is it
reasonable to conclude that any of the trucks were driven more than 70,000
miles? Explain.
38. The mean amount purchased by a typical customer at
Churchill’s Grocery Store is $23.50 with a standard deviation of $5.00. Assume
the distribution of amounts purchased follows the normal distribution. For a
sample of 50 customers, answer the following questions.
1. What is
the likelihood the sample mean is at least $25.00?
2. What is
the likelihood the sample mean is greater than $22.50 but less than $25.00?
3. Within
what limits will 90 percent of the sample means occur?
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