Random Variables Flashcards
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
D. 3
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
B. # of soldiers in the troop
how many ways are there in tossing two coins once?
a. 4
b. 3
c. 2
d. 1
C. 2
it is a numerical quantity that is assigned to the outcome of an experiment
a. random variable
b. variable
c. probability
d. probability distribution
A. random variable
it is the central or average of its corresponding probability mass function
a. mean
b. variance
c. standard deviation
d. probability
A. mean
what is the mean outcome if a pair of die is rolled once
C
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
C. 2
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
A. 1
what is another term for normal distribution?
a. Gaussian
b. Poisson
c. Bernoulli
d. Probability
A Gaussian
what is the total area in the distribution under the normal curve
a. 0
b. 1
c. 2
d. 3
B. 1
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
C. mean and the standard deviation
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
A. mean
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
B. 95.4
how many standard deviations are there in each inflection point
a. 0
b. 1
c. 2
d. 3
B. 1
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
A. -1.25
it refers to the entire group that is under study or investigation
a. population
b. sample
c. random sampling
d. subset
A. population
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
B. sample
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
A. systematic
it is sometimes called area sampling
a. systematic
b. lottery
c. stratified
d. cluster
D. cluster
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
C. random
which sample size gives a smaller standard error of the mean according to central limit theorem?
a. 10
b. 15
c. 25
d. 35
D. 35
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
A the sample size is large
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
D. 40
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
B. 1.5
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
A. it becomes narrower and more normal
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
B. 5.59
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
a. 12.1
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
C. normal
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
A. 19.32 in
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
A. 0.7088
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
D. -1.23
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
A. 0.8907
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
D. hypothesis
what is the statistical method used in making decisions using experimental data?
a. simple analysis
b. analytical testing
c. hypothesis testing
d. experimental testing
C, hypothesis testing
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
B. Ha is not equal to 100
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
B. the mean of a population is equal to 75
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
B. we reject a null hypothesis that is true
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
D. we fail to reject a null hypothesis that is false
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
A. Ho is true; reject Ho
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
B. Ha<100
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%
A. 1%
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
a. 𝐻𝑎 < 100
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
d. – 1.728
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.
A. It lies in the rejection region, 𝐻𝑜 must be rejected.
.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�
