Assignment:
1. A manufacturer of VCRs purchases a particular microchip, called the LS-24 from three suppliers; Hall Electronics, Schuller Sales, and Crawford Components. Thirty percent of the LS-24 chips are purchased from Hall Electronics, 20 percent from Schuller Sales, and the remaining 50 percent from Crawford Components. The manufacturer has extensive histories on the three suppliers and knows that 3 percent of the LS-24 chips from Hall Electronics are defective, 5 percent from Schuller Sales are defective and 4 percent of the chips from Crawford Components are defective. When the LS-24 chips arrive at the manufacturer, they are placed directly in a bin and not inspected or otherwise identified by supplier. A worker selects a chip for installation in a VCR and finds it defective. What is the probability that the selected chip was manufactured by Schuller Sales?
2. The following are the numbers of miles (to the nearest thousand) showing on the odometers of a sample of 105 automobiles to a dealer for trade-in.
38 34 56 43 32 40 40 41 30 55 41 37 41 41 40 48 46 33 35 33 34 51 48
43 29 30 32 37 37 48 30 37 50 55 30 46 51 35 43 35 38 43 27 36 40 43
41 32 45 45 30 31 32 37 37 32 41 40 36 45 37 36 48 40 32 55 43 36 40
33 51 37 35 35 36 36 30 37 29 40 36 47 43 37 51 48 35 46 40 34 35 31
34 45 32 37 40 35 29 38 30 41 48 50
For these data:
a. Construct a frequency distribution
b. Draw a histogram
c. Compute the mean
d. Compute the median
e. Compute the variance and standard distribution
3. A long-term study of accidents at the Retread Shoe Factory led management to conclude that the average number of accidents per person per year was 0.3. What is the probability that a randomly selected employee will:
a. Not have an accident within the coming year
b. Will have at least 1 accident in the coming year
c. Will have exactly 1 accident in the coming year
d. Will have between 2 and 4 accidents in the coming year
4. The Falcon Insurance Company founded in 1885, found that 8% of its claims are for damages resulting from burglaries. What is the probability that a random sample of 20 claims will contain 5 or fewer that is for burglary damages?
5. A large mail-order department store finds that approximately 17% of all purchases are returned for credit. If the store sells 100,000 different items this year, about how many items will be returned? Find the standard deviation
6. In a recent study it was found that in one town the number of hours that a typical 10-year-old child watches television per week is normally distributed with a mean of 12 hours and a standard deviation of 1.5 hours. If Gary is a typical 10-year-old child in this town, what is the probability that he watches between 9 and 14 hours of television per week?
7. A survey of 16 taxi drivers found that the average tip they receive is 90 cents with a standard deviation of 8 cents. Find a 95% confidence interval for estimating the average amount of money that a taxi driver receives as a tip.
8. A light bulb company claims that the 60-watt light bulb it sells has an average life of 1000 hours with a standard deviation of 75 hours. Sixty-four new light bulbs were allowed to burn out to test this claim. The average lifetime of these bulbs was found to be 975 hours. Does this indicate that the average life of a bulb is not 1000 hours?
9. A new weight-reducing pill is being sold in a Midwestern city. The manufacturer claims that any overweight person who takes this pill as directed will lose 15 pounds within a month. To test this claim, a doctor gives this pill to six overweight people and finds that they lose an average of only 12 pounds with a standard deviation of 4 pounds, Can we reject the manufacturer's claim?
10. The Marvo Insurance Company finds that the average number of auto accident claims involving uninsured motorists filed against the company is two per day. What is the probability of:
a. No claims involving uninsured motorists are filed against the company?
b. At most two claims are filed
c. At least two claims are filed
d. Between 3 and five, inclusive, claims are filed
11. One nationwide pizza delivery chain reports that 25% of its order takers are female. Moreover, 20% of its male orders takers and 15% of its female order takers attend college. If an order taker that attends college is randomly selected, what is the probability that the order taker is female?
12. Environmentalists have accused a large company in the eastern United States of dumping nuclear waste material into a local river. The probability that either the fish in the river or the animals that drink from the river will die is 11/21. The probability that only the fish will die is 1/3, and the probability that only the animals that drink from the river will die is 2/7. What is the probability that both the fish and the animals that drink from the river will die?
13. A local law firm that employs over 200 attorneys has established a computer "help desk". After several years of operation, the Help Desk Manager finds that the average number of calls to the help desk is 7 calls per hour. What is the probability that on a particular workday, the help desk will receive:
a. at least three calls per hour
b. at the most three calls per hour c. exactly three calls per hour
14. Ninety percent of the graduates of State University who apply to a particular medical school are admitted. This year, six graduates from State University have applied for admission to the medical school. What is the probability that only four of them will be accepted?
15. A certain type of crossbred cow, when mated with a sire of the same genetic type, will produce a white-faced red calf 25% of the time, whereas the remaining 75% of the time the calf will have other color combinations. If 12 of these cows are selected at random, what is the probability that exactly 5 of them will have white-faced red calves?
16. A biochemist mixed six chemicals together in a solution and created a new synthetic drug. Unfortunately, the biochemist does not remember the order in which the chemicals were introduced into the solution. It is decided to repeat the experiment. How many possibilities are there?
17. What is the probability of drawing a five from a deck of cards without Jokers or the probability of drawing a heart from the same deck of cards without Jokers?
18. Find the percentage of z-scores in a standard normal distribution that are above z =0.9854.
19. According to an article in the February 2006 issue of Consumer Reports, the U.S. Energy Information Administration reports that the life expectancy of a typical refrigerator is normally distributed with a mean life of 15 years and a standard deviation of 3.7 years. Find the probability that a randomly selected refrigerator will last more than 17 years.
20. Police Department Officials indicate that the average number of homicides per day in New York City is 5.4. What is the probability that on any given day there will be:
a. At the most four homicides? b. Exactly four homicides?
Scenario:
You are an associate assigned to the claims department of a major insurance company. A policy holder has had an accident with his classic 1968 Oldsmobile Cutlass Supreme.
At issue is the consideration of his brakes. Recently, he was driving down the road and was apparently unable to stop in time when a woman driving a 2004 Porsche Boxster "S" pulled out in front of him; subsequently, he "T-boned" the Porsche. Injured in the accident were the, driver of the Porsche, who was 7 months pregnant with twins and her elderly mother-in-law who has cerebral palsy; both of which were from out of town.
Now with their only means of transportation "totaled" they are stranded.
The Porsche driver's insurance company, which is USAA, contends that your policy holder is at fault because his car was not up to current standards. There seems to be a difference in the braking distance between vintage brake shoes and current ones.
Your policy holder is a self proclaimed, "shade tree" mechanic and a classic car enthusiast. As a matter of fact, he once owned a rather successful auto mechanic business and is now the President of the State of Florida Oldsmobile Club which has a substantial lobby in Tallahassee.
Your boss decided that because you are enrolled in a statistics class you should be pressed into service to assist and, as such, you have questioned the policy holder extensively. From your investigation you discover that he does his own work and recently replaced his brakes with a vintage brand of asbestos brake shoes. The contention is that modern brake shoes stop a vehicle which is traveling at 35 mph (which your policy holder was proven to be doing) at 20.5 feet, give or take one foot either side.
Your company's research department gathered the following in support:
Out of 42 sets available, worldwide, of vintage asbestos brake shoes, 20 were selected for testing. Below are the results:
23.2 18.1 19.2 20.3 23.0
26.0 24.6 16.9 17.3 23.4
28.6 17.2 23.2 18.7 19.6
20.8 24.2 25.0 19.8 17.6
Questions;
A. What is the percentage of these pads that fall within the current and more modern parameters?
B. Arrange this data in class intervals and construct a Frequency Distribution chart.
C. Construct a confidence interval to predict the boundaries of this parameter.
D. Your policy holder actually contends that the vintage brake shoes exceed the modem standards. Is there evidence that would suggest he is correct?
E. Assuming that the stopping distance between the vintage brake shoe and the modem equivalent is the same, what is the probability that either one tested will stop a vehicle of this size or larger, within 5 feet of the true mean?
F. What is the probability that the difference between the stopping distance with the vintage brake pads and the stopping distance of the newer style brake pads being as large as reported or larger if there is no difference in the true stopping distance averages between the two styles?