# Multiple choice questions from random variables

1) A test consists of 690 true or false questions. If the student guesses on each question, what is the mean number of correct answers?

A) 0 B) 138 C) 345 D) 690

2) IQ test scores are normally distributed with a mean of 101 and a standard deviation of 13. An individual's IQ score is found to be 103. Find the z-score corresponding to this value.

A) 0.15 B) 6.50 C) -0.15 D) -6.50

3) The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 4.0 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 2.5 and 5.0 minutes to find a parking spot in the library lot.

A) .4938 B) .7745 C) .0919 D) .2255

4) In a recent survey, 61% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 5 of them favor the building of the police substation.

A) 0.211 B) 0.357 C) 0.035 D) 0.610

5) True or False: The proportion of the population that has certain characteristics is the same as the probability that a randomly selected individual of the population has these same characteristics.

A) True B) False

6) For a standard normal curve, find the z-score that separates the bottom 70% from the top 30%.

A) 0.52 B) 0.12 C) 0.47 D) 0.98

7) A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution below:

Price $10.00 $12.50 $15.00

Probability 0.25 0.4 0.35

Suppose the mean cost of the rats turned out to be $12.75 per week. Interpret this value.

A) The rat cost that occurs more often than any other is $12.75.

B) Most of the weeks resulted in rat costs of $12.75.

C) The average cost for all weekly rat purchases is $12.75.

D) The median cost for the distribution of rat costs is $12.75.

8) The amount of corn chips dispensed into a 32-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 32.5 ounces and a standard deviation of 0.2 ounce. What chip amount represents the 67th percentile for the bag weight distribution?

A) 32.63 ounces B) 32.09 ounces C) 32.59 ounces D) 32.13 ounces

9) Which of the below is not a requirement for binomial experiment?

A) The probability of success is fixed for each trial of the experiment.

B) For each trial there are two mutually exclusive outcomes.

C) The trials are mutually exclusive.

D) The experiment is performed a fixed number of times.

10) The area under a standard normal density curve with mean of 0 and standard deviation of 1 is

A) ? + 2(3ô???) B) Infinite C) 1 D) ? + 3ô???

11) A test consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass the test a student must get 60% or better on the test. If a student randomly guesses, what is the probability that the student will pass the test?

A) 0.377 B) 0.060 C) 0.205 D) 0.006

12) The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3.0 minutes.

A) .3085 B) .2674 C) .3551 D) .1915

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#### Solution Summary

The solution gives answers to multiple choice questions from normal and binomial random variables and probability.

Statistics Multiple choice: The Exhibits are the sentences or tables of numbers below the Exhibit number. Total 15 multiple choice questions. In the following multiple-choice questions, circle the correct answer and give 1-3 line defense for your choice:

16. If a coin is tossed three times, the likelihood of obtaining three heads in a row is

a. zero

b. 0.500

c. 0.875

d. 0.125

e. None of the above answers is correct.

17. If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then

P(A|B) =

a. 0.05

b. 0.0325

c. 0.65

The following represents the probability distribution for the daily demand of microcomputers at a local store.

Demand Probability

0 0.1

1 0.2

2 0.3

3 0.2

4 0.2

Exhibit 5-2

The student body of a large university consists of 60% female students. A random sample of 8 students is selected.

20. Refer to Exhibit 5-2. What is the probability that among the students in the sample exactly two are female?

a. 0.0896

b. 0.2936

c. 0.0413

d. 0.0007

e. None of the above answers is correct.

21. Refer to Exhibit 5-2. What is the probability that among the students in the sample at least 7 are female?

a. 0.1064

b. 0.0896

c. 0.0168

d. 0.8936

d. None of the above answers is correct.

Exhibit 5-4

Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.

Exhibit 5-4

Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.

27. Refer to Exhibit 5-4. The probability that the sample contains 2 female voters is

a. 0.0778

b. 0.7780

c. 0.5000

d. 0.3456

e. None of the above answers is correct.

28. Refer to Exhibit 5-4. The probability that there are no females in the sample is

a. 0.0778

b. 0.7780

c. 0.5000

d. 0.3456

e. None of the above answers is correct.

34. Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?

a. the experiment has a sequence of n identical trials

b. exactly two outcomes are possible on each trial

c. the trials are dependent

d. the probabilities of the outcomes do not change from one trial to another

e. all are characteristics of a binomial probability experiment

35. Which of the following is not a property of a binomial experiment?

a. the experiment consists of a sequence of n identical trials

b. each outcome can be referred to as a success or a failure

c. the probabilities of the two outcomes can change from one trial to the next

d. the trials are independent

e. All of the above answers are correct.

36. A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?

a. 0.0004

b. 0.0038

c. 0.10

d. 0.02

e. 0.00

37. Z is a standard normal random variable. The P(-1.96  Z  -1.4) equals

a. 0.8942

b. 0.0558

c. 0.475

d. 0.4192

e. None of the above answers is correct.

38. Z is a standard normal random variable. The P(1.20  Z  1.85) equals

a. 0.4678

b. 0.3849

c. 0.8527

d. 0.0829

e. None of the above answers is correct.

39. Z is a standard normal random variable. The P (-1.20  Z  1.50) equals

a. 0.0483

b. 0.3849

c. 0.4332

d. 0.8181

e. None of the above answers is correct.

40. Z is a standard normal random variable. Compute the following probability.

P(Z = 2.56)

A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

a. 0.2592

b. 0.0142

c. 0.9588

d. 0.7408

e. 0.0000

31. Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is

a. 20

b. 16

c. 4

d. 2

e. None of the above answers is correct.

32. If you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of 4 successes in 15 trials, the correct probability function to use is the

a. standard normal probability density function

b. normal probability density function

c. Poisson probability function

d. binomial probability function

e. None of the above answers is correct.

33. Which of the following statements about a discrete random variable and its probability distribution are true?

a. Values of the random variable can never be negative.

b. Some negative values of f(x) are allowed as long as f(x) = 1.

c. Values of f(x) must be greater than or equal to zero.

d. The values of f(x) increase to a maximum point and then decrease.

e. None of the above answers is correct.