1. On average, 6 birds hit the Washington Monument and are killed each week. Bill Garcy,
an official of the National Parks Services, has requested that congress allocate funds for
equipment to scare birds away from the monument. A Congressional subcommittee has
replied that funds can not be allocated unless the probability of more than three birds
being killed in any week exceeds 0.8. Will the funds be allocated?
2. One study on managers’ satisfaction with management tools reveals that 62% of all
managers use self –directed work teams as a management tool. Suppose 80 managers
selected randomly are interviewed. What is the probability that fewer than 35 use self –
directed work teams as a management tool?
3. The mean number of hours of flying time for pilots at Continental Airlines is 55 hours per
month. Assume that this mean was based on actual flying times for a sample of 100
Continental pilots and that the sample standard deviation was 8.5 hours. What is the 95%
confidence interval estimate of the population mean flying time for the pilots?
4. Suppose a US car rental firm wants to estimate the average number of miles travelled per
day by each of its cars rented in California. A random sample of 200 cars rented in
California reveals that the sample mean travel distance per day is 80.0 miles, with a
sample standard deviation of 15.3 miles. Compute a 95% confidence interval to estimate
µ.
5. The rank of the 17 students in two subjects A and B, are given below. The two numbers
within brackets denote the ranks of a student in A and B subjects respectively.
(1, 10), (2, 7), (3, 2), (4, 6), (5, 4), (6, 8), (7, 3), (8, 1), (9, 11), (10, 16), (11, 9), (12, 5),
(13, 17), (14, 12), (15, 13), (16, 14), (17, 15). Find Spearman’s rank correlation
coefficient.
6. The American Association of individual investors publishes an annual guide to the top
mutual funds. Table given below contains their rating of the total risk for 32 categories of
mutual funds.
Total Risk
Number of funds Categories
Low
8
Below Average
6
Average
4
Above Average
6
High
8
a. Let x = 1for low risk up through x=5 for high risk, and develop a probability
distribution for level of risk.
b. What are the expected value and variance for total risk?
c. It turns out that 14 of the fund categories were bond funds. For the bond funds, 8
categories were rated low, 4 were rated below average, and 2 were rated average.
Compare the total risk of the bond funds with the 18 categories stock funds.
7. An industrial sewing machine uses ball bearing that are targeted to have a diameter of
0.75 inch. The lower and upper specification limits under which the ball bearing can
operate are 0.74 inch and 0.76 inch, respectively. Past experience has indicated the actual
mean diameter of the ball bearing 0.753 with a standard deviation of .005 inch. What is
the probability that a ball bearing is
a. Between the target and the actual mean?
b. Between the lower specification limits and the target?
c. 85% of the diameters are greater than what value?
Docsity.com
