Assignments2 solutions: Due by Midnight Sunday, February 17, 2013
(dropbox of week 2) (Chapters 4, 5, and 6): Total 70 points. Show work
True/False (one point each)Chapter 4
1. . Events whose union has the probability equal to 1 are called Exhaustive events.
2. If events A and B are mutually exclusive, then P(A/B) is always equal to zero.
3. If events A and B are independent, then P(A/B) is always equal to zero.
Chapter 54. If the probability of success is 0.2 and the number of trials in a binomial distribution is 400, then its standard deviation is 8.
5. If a fair coin is tossed 100 times, then the variance of the random variable defined as the number of heads is exactly five.
6. If a fair coin is tossed 20 times then the probability of exactly 10 Tails is less than 17 percent.
Chapter 67.The number of defective pencils in a lot of 1000 is an example of a discrete random variable.
8.For a continuous distribution, P(X = 100) is greater than P(X9.A continuous variable may not be Normally distributed.
10.The mean of a standard normal distribution is not equal to 1.
11. If the sample size is 1000, we can safely use the normal approximation to binomial even for small p.
12. For a binomial probability experiment, if p is 0.1 and n is only 150, we cannot use the normal approximation to the binomial distribution without continuity correction.
Multiple Choice (2 points each)Multiple Choice (Chapter 4)
1. Two mutually exclusive events having positive probabilities are ______________ dependent.
A.Never
B.Always
C.Sometimes
2. If P(A)>0 and P(B)>0 and events A and B are independent, then:
A.
P(A)=P(B)P((
A|B)
)=P(A)C.
P(A
B)=0D.
P(A
B)=P(A)Chapter 53. In a study conducted by UCLA, it was found that 25% of college freshmen support increased military spending. If 6 college freshmen are randomly selected, find the probability that more than 3 support increased military spending
A.0.0376
B.0.1318
C.0.8682
D.0.9624
4. A fair die is rolled 10 times. What is the probability that an even number (2, 4 or 6) will occur between 2 and 4 times (inclusive)?
A.0.6123
B.0.1709
C.0.1611
D.0.3662
E.0.3223
5.Which one of the following statements is not a necessary assumption of the binomial distribution?
A.Sampling is with replacement
B.The experiment consists of n identical trials
C.The probability of success remains constant from trial to trial
D.Trials are independent of each other
E.Each trial results in one of two mutually exclusive outcomes
6.If p=.6 and n=10, then the corresponding binomial distribution is
A.Right skewed
B.Left skewed
C.Symmetric
D.Bimodal
7. A fair die is rolled 36 times. What is the standard deviation of the even number (2, 4 or 6) outcomes?
A.18
B.6
C.4
D.3
8.A fair die is rolled 12 times. What is the probability that an odd number (1, 3 or 5) will occur less than 6 times?
A.0.1934
B.0.2256
C. 0.6128
D.0.3872
E.0.5000
9. In the most recent election, 20% of all eligible college students voted. If a random sample of 20 students were surveyed:
Find the probability that at least five students voted in the election.
A.0.1746
B.0.2182
C. 0.3704
D.0.6296
Chapter 610. The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population, what is the probability that it will weigh more than 904 grams?
A. 0.3849
B. 0.7698
C. 0.2302
D. 0.8849
E. 0.1151
11.The area under the normal curve between z=0 and z=1 is ________________ the area under the normal curve between z=1 and z=2.
A. Equal to
B. Less than
C. Greater than
D.A, B or C above dependent on the value of the mean
E.A, B or C above dependent on the value of the standard deviation
12. If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour
A.Is greater than the proportion of workers earning less than $18 per hour
B.Is less than 50%
C.Is less than the proportion of workers earning more than the mean wage $15
D.Is greater than the proportion earning less than $13 per hour
E. Cannot tell without knowing the standard deviation
13. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years 14 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that at least 30 accounts will be classified as delinquent?
A.31.86%
B.18.14%
C.81.86%
D.63.72%
E.75.84%
14.Which of the following statements is not a property of the normal probability distribution?
A.The normal distribution is symmetric
B.Exactly 90% of all possible observed values of the random variable x are within plus or minus two standard deviations of the population mean
C.The mean, median and mode are equal
D.The area under the normal curve to the right of the mean is equal to the area under the normal curve to the left of the mean
E.All of the above answers are properties of the normal distribution
15. According to a hospital administrator, historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospital patients has just been conducted. What is the probability that less than 70 patients will not be satisfied with the after-surgery care?
A. 89.44%
B. 39.44%
C. 10.56%
D. 78.88%
E. 84.49%
Essay Type (each question carries 4 points)
Chapter 41. At a college, 60 percent of the students are female and 30 percent of the students receive a grade of C. About 45 percent of the students are neither male nor C students. Use this contingency table.
Gender\C or not C
|
C
|
Not C
?
|
Female (F)
|
0.45
|
0.60
|
Male (M)
|
0.30
|
If a student selected at random is a “
Not C”student, what is the probability that the student is male?
2. About 25% of the customers of a store buy cigars and 35 % of customers buybeer. About 10% buy both. The contingency table is given below.
Beer |
No Beer |
Cigars |
0.10 |
0.25 |
No cigar |
0.35 |
Determine the probability that a customer will buy only one of these items: either cigar or beer
but not both.
3. Four employees who work as drive-through attendees at a local fast food restaurant are being evaluated. As a part of quality improvement initiative and employee evaluation these workers were observed over three days. One of the statistics collected is the proportion of time employee forgets to include a napkin in the bag. Related information is given in the table.
You just purchased a dinner and found that there is no napkin in your bag, what is the probability that Clay has prepared your order?
Chapter 54. In a study conducted for the State Department of Education, 30% of the teachers who left teaching did so because they were laid off. Assume that we randomly select 15 teachers who have recently left their profession. Find the probability that at least 6 of them were laid off.
5.The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 25%. If 15 calculators are selected at random, what is the probability that more than 5 of the calculators will be defective?
Chapter 66.If x is a binomial random variable where n = 100 and p = .1, find the probability that x is more than or equal to 12
using the normal approximation to the binomial.
7.The weight of a product is normally distributed with a standard deviation of .8 ounces. What should the average weight be if the production manager wants no more than 5% of the products to weigh more than 10 ounces?