Part-1

1. Mutually exclusive events are also independent. False

2. If events A and B are independent, then the probability of A given B, that is, P(A|B) is generally not equal to 0.False

3. Events that have no sample space outcomes in common and, therefore cannot occur simultaneously are referred to as independent events.

4. In a binomial distribution the random variable X is continuous.

5. The variance of the binomial distribution is √np(1-p)

6. The binomial experiment consists of n independent, identical trials, each of which results in either success or failure and the probability of success on any trial must be the same.

7. The mean and variance are the same for a standard normal distribution.

8. In a statistical study, the random variable X=1, if the house is colonial and X=0 if the house is not colonial, then it can be stated that the random variable is discrete.

9. For a discrete random variable which can take values from 0 to 150, P(X ≤ 100) is greater than P(X<100).

10. The number of defective pencils in a lot of 1000 is an example of a continuous random variable.

11. All continuous random variables are normally distributed.

Part-2

1. Two mutually exclusive events having positive probabilities are ______________ dependent.

A. Sometimes
B. Always
C. Never

2. ___________________ is a measure of the chance that an uncertain event will occur.

A. Random experiment
B. Sample Space
C. Population
D. Probability
E. Probability Distribution

3. In which of the following cases can we say that A1 and A2 are complements?

A. A1 and A2 are mutually exclusive
B. A1 and A2 are totally exhaustive
C. A1 and A2 are independent
D. P(A1/A2)=P(A1)
E. If both A andB are satisfied

4. In which of the following are the two events A1 and A2, independent?

A. A1 and A2 are mutually exclusive
B. The intersection of A1 and A2 is zero
C. The probability of A or B is the sum of the individual probabilities
D. P(A1/A2) = P(A1)
E. Choices A and B

5. If p=.45 and n= 15, then the corresponding binomial distribution is

A. Left skewed
B. Right skewed
C. Symmetric
D. Bimodal

6. Which of the following is a valid probability value for a random variable?

A. -0.7
B. 1.01
C. 0.2
D. All of the above

7. Which of the following statements about the binomial distribution is not correct?

A. Each trial results in a success or failure
B. Trials are independent of each other
C. The probability of success remains constant from trial to trial
D. The experiment consists of n identical trials
E. The random variable of interest is continuous

8. Which one of the following statements is an essential assumption of the binomial distribution?

A. Sampling must be done with replacement
B. The probability of success remains constant from trial to trial
C. The probability of success is equal to the probability of failure in each trial
D. The number of trials must be greater than 2
E. The total number of successes in an experiment cannot be zero

9. A fair die is rolled 10 times. What is the probability that an even number (2, 4 or 6) will occurless than 3?

A. 0.0547
B. 0.1719
C. 0.8281
D. 0.1172
E. 0.9453

10. 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 12 teachers who have recently left their profession. Find the probability that 5 or more of them were laid off.
A. 0.2311
B. 0.7237
C. 0.2763
D. 0.7689
E. 0.4925

11. The probability or the area under the normal curve between Z =2and Z =3 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 normal random variable X has a mean of µ and a standard deviation σ, then (X-µ)/σ has a mean and standard deviation, respectively:

A. 1 and 0
B. X ¯and s
C. µ and σ
D. 0 and 1

13. 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. 0.8849
B. 0.3849
C. 0.1151
D. 0.7698
E. 0.2302

14. The normal approximation of the binomial distribution is appropriate when:
A. np ≥ 10
B. n(1-p) ≥ 10
C. np ≤ 10
D. np ≥ 10 and n(1-p) ≥ 10
E. n(1-p) ≤ 10 and np ≤ 10

Part-3

1. At a college, 60 percent of the students are female and 30 percent of the students receive a grade of C. About 42 percent of the students are female and not C students. Use this contingency table.

If a randomly selected student is a C student, what is the probability the student is 2. A and B are independent events. Moreover, P(A)= 0.5 and P(B)= 0.6. Determine P(A B), that is, P(A or B)

3. The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. If 14 calculators are selected at random, what is the probability that 4 or lessof the calculators will be defective?
4. An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the probability is 0.60 that troubles in a residential service can be repaired on the same day. For the first seven troubles reported on a given day, what is the probability that 4 or more troubles will be repaired on the same day?

5. Given the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet, what is the probability he throws it:  Between 45 feet and 54 feet?

6. If x is a binomial random variable where n=100 and p=.5, find the probability that x is more than or equal to 44 using the normal approximation to the binomial.