Random Variables

Question 1

if two coins are tossed once, which is NOT possible value of the random variable for the number of heads
a. 0
b. 1
c. 2
d. 3

Answer 1

D. 3

Question 2

which of the following is a discrete random variable
a. length of wire ropes
b. # of soldiers in the troop
c. amount of paint used in repainting the building
d. voltage of car batteries

Answer 2

B. # of soldiers in the troop

Question 3

how many ways are there in tossing two coins once?
a. 4
b. 3
c. 2
d. 1

Answer 3

C. 2

Question 4

it is a numerical quantity that is assigned to the outcome of an experiment
a. random variable
b. variable
c. probability
d. probability distribution

Answer 4

A. random variable

Question 5

it is the central or average of its corresponding probability mass function
a. mean
b. variance
c. standard deviation
d. probability

Answer 5

A. mean

Question 6

what is the mean outcome if a pair of die is rolled once

Answer 6

C

Question 7

find the mean of the probability distribution involving the random variable x that gives the number of heads that appear after tossing 4 coins once
a. 4
b. 3
c. 2
d. 1

Answer 7

C. 2

Question 8

the probabilities that a printer produces 0,1,2, and 3 misprints are 42%, 28%,18%, and 12% respectively. what is the mean value of the random variable
a. 1
b. 2
c. 3
d. 4

Answer 8

A. 1

Question 9

what is another term for normal distribution?
a. Gaussian
b. Poisson
c. Bernoulli
d. Probability

Answer 9

A Gaussian

Question 10

what is the total area in the distribution under the normal curve
a. 0
b. 1
c. 2
d. 3

Answer 10

B. 1

Question 11

which of the following is the parameter of normal distribution
a. mean
b. standard deviation
c. mean and standard deviation
d. none of the above

Answer 11

C. mean and the standard deviation

Question 12

the graph of a normal distribution is symmetrical about the __
a. mean
b. standard deviation
c. mean and standard deviation
d. none of the above

Answer 12

A. mean

Question 13

what percent of the area under a normal curve is within 2 standard deviations?
a. 68.3
b. 95.4
c. 99.7
d. 100

Answer 13

B. 95.4

Question 14

how many standard deviations are there in each inflection point
a. 0
b. 1
c. 2
d. 3

Answer 14

B. 1

Question 15

A random variable X has a mean of 12 and a standard deviation of 3.2. what is the corresponding z-score for x=8?
a. -1.25
b. -1.50
c. -1.75
d. -2.25

Answer 15

A. -1.25

Question 16

it refers to the entire group that is under study or investigation
a. population
b. sample
c. random sampling
d. subset

Answer 16

A. population

Question 17

it is a subset taken from a population, either by rando, or nonrandom sampling techniques
a. population
b. sample
c. random sampling
d. quota sampling

Answer 17

B. sample

Question 18

what sampling technique in which members of the population are listed and samples are selected in intervals called sample intervals
a. systematic
b. lottery
c. stratified
d. cluster

Answer 18

A. systematic

Question 19

it is sometimes called area sampling
a. systematic
b. lottery
c. stratified
d. cluster

Answer 19

D. cluster

Question 20

it refers to a part of the sampling technique where each sample point has an equal chance of being selected
a. systematic
b. lottery
c. random
d. quota

Answer 20

C. random

Question 21

which sample size gives a smaller standard error of the mean according to central limit theorem?
a. 10
b. 15
c. 25
d. 35

Answer 21

D. 35

Question 22

the central limit theorem says that the sampling distribution of the sample mean is approximately normal if __
a. the sample size is large
b. all possible sample are selected
c. the standard error of the sampling mean is small
d. none of the above

Answer 22

A the sample size is large

Question 23

sample size of 25 are selected from a population with a mean of 40 and a standard deviation of 7.5. what is the mean of the sampling distribution of sample means?
a. 7.5
b. 8
c. 25
d. 40

Answer 23

D. 40

Question 24

sample size of 25 are selected from a population with a mean of 40 and a standard deviation of 7.5. what is the standard error of the sampling distribution of sample means?
a. 0.3
b. 1.5
c. 7.5
d. 8

Answer 24

B. 1.5

Question 25

what happens to the shape of a sampling distribution of sample means as n increases? a. it becomes narrower and more normal b. it becomes wider and more normal c. it becomes narrower and bimodal d. it becomes wider and skewed right

Answer 25

A. it becomes narrower and more normal

Question 26

in a group of 20 randomly selected unicorns, the mean is 1,000 and the standard deviation is 25, what is the standard deviation of the sampling distribution? a. 25 b. 5.59 c. 4 d. 1.25

Answer 26

B. 5.59

Question 27

a group 625 students hs a mean age of 15.8 years with a standard deviation of 0.6 years. the ages are normally distributed. what is the probability that a randomly selected students are older than 16.5 years? a. 12.1 b. 86.4 c. 87.9 d. 13.6

Answer 27

a. 12.1

Question 28

if the random samples are larger, what is the shape of the sampling distribution of the mean? a. skewed to the left b. skewed to the right c. normal d. rectangular

Answer 28

C. normal

Question 29

what is the average precipitation of 5 randomly selected years for the first 7 months? a. 19.32 in b. 22.4 in c. 20.52 in d. 15.56 in

Answer 29

A. 19.32 in

Question 30

what is the probability that a randomly selected year will have precipitation greater than 18 in for the first 7 months? a. 0.7088 b 0.8523 c. 0.4562 d. 0.1258

Answer 30

A. 0.7088

Question 31

compute the z-score for precipitation of 18 in for 5 randomly selected years for the first 7 months? a. -0.55 b. 0.55 c. 1.23 d. -1.23

Answer 31

D. -1.23

Question 32

what is the probability of 5 randomly selected years will have an average precipitation greater than 18 inches for the first 7 months? a. 0.8907 b. 0.2587 c. 0.4156 d. 0.2879

Answer 32

A. 0.8907

Question 33

it is a proposed explanation, assertion, or assumption about a population parameter or about the distribution of a random variable. a. decision b. statistic c. probability d. hypothesis

Answer 33

D. hypothesis

Question 34

what is the statistical method used in making decisions using experimental data? a. simple analysis b. analytical testing c. hypothesis testing d. experimental testing

Answer 34

C, hypothesis testing

Question 35

which of the following describes an alternative hypothesis using 2-tailed test a. Ha= 100 b Ha is not equal to 100 c. Ha > 100 d. Ha < 100

Answer 35

B. Ha is not equal to 100

Question 36

which of the following would be and appropriate null hypothesis a. the mean of a sample is equal to 75 b. the mean of a population is equal to 75 c. the mean of sample is not equal to 75 d. the mean of a population is not equal to 75

Answer 36

B. the mean of a population is equal to 75

Question 37

when is a type I error committed? a. we reject a null hypothesis that is false b. we reject a null hypothesis that is true c. we fail to reject a null hypothesis that is true d. we fail to reject a null hypothesis that is false

Answer 37

B. we reject a null hypothesis that is true

Question 38

when is a type ll error committed? a. we reject a null hypothesis that is true b. we reject a null hypothesis that is true c. we fail to reject a null hypothesis that is true d. we fail to reject a null hypothesis that is false

Answer 38

D. we fail to reject a null hypothesis that is false

Question 39

which of the following is a type l error? a. Ho is true; reject Ho b. Ho is false; reject Ho c. Ho is true, fail to reject Ho d. Ho is false; fail to reject Ho

Answer 39

A. Ho is true; reject Ho

Question 40

which of the following describes an alternative hypothesis in a left-tailed test? a. Ha>100 b. Ha<100 c. Ha=100 d. Ha is not equal to 100

Answer 40

B. Ha<100

Question 41

Which of the following must be used as the level of significance if we want a higher possibility of correct decision? a. 1% b. 5% c. 10% d. 25%

Answer 41

A. 1%

Question 42

Which of the following would be an appropriate alternative hypothesis for one-tailed test? a. 𝐻𝑎 < 100 b. 𝐻𝑎 = 100 c. 𝐻𝑎 ≥ 100 d. 𝐻𝑎 ≤ 100

Answer 42

a. 𝐻𝑎 < 100

Question 43

Using a left-tailed test, which of the following value of z falls in the rejection region where the critical value is – 1.725? a. – 1.700 b. – 1.715 c. – 1.724 d. – 1.728

Answer 43

d. – 1.728

Question 44

If the computed z-value is 2.015 and the critical value is 1.833, which of the following statements could be true? a. It lies in the rejection region, 𝐻𝑜 must be rejected. b. It lies in the rejection region, we failed to reject 𝐻𝑜. c. It lies in the non-rejection region, 𝐻𝑜 must be rejected. d. It lies in the non-rejection region, we failed to reject 𝐻𝑜.

Answer 44

A. It lies in the rejection region, 𝐻𝑜 must be rejected.

Question 45

.If the computed z-value is – 1.290 and the critical value is – 2.571, which of the following statements could be true? a. It lies in the rejection region, 𝐻𝑜 must be rejected. b. It lies in the rejection region, we failed to reject 𝐻𝑜. c. It lies in the non-rejection region, 𝐻𝑜 must be rejected. d. It lies in the non-rejection region, we failed to reject 𝐻�