MCQ in Probability and Statistics Part 1 | Licensure Exam for Teachers 2022

(Last Updated On: July 20, 2022)

This is the LET Reviewer 2021, Multiple Choice Questions in Probability and Statistics Part 1 as one coverage of Mathematics examination as part of Licensure Examinations for Teachers (LET). The exam is divided into two classifications. First is the elementary level exam which covers topics from General Education (GenEd) 40% and Professional Education (ProfEd) 60%. Secondly is the secondary level which covers GenEd 20%, ProfEd 40% and area of specialization 40%. I assume you are looking for a reviewer that will help you achieve your goal to become a professional License teacher very soon. Yes, you are in the right place to make your dream come true. Make sure to familiarize each and every questions to increase the chance of passing the Licensure Examinations for Teachers (LET).

General Education Math Coverage

For the Mathematics portion of the Gen Ed exam, here’s the coverage:

• Fundamentals of Math
• Plane Geometry
• Elementary Algebra
• Probability and Statistic

Major in Mathematics Coverage

For our future secondary education teachers, here’s the exam coverage for your area of specialization:

• arithmetic and number theory
• business math
• basic and advanced algebra
• plane and solid geometry
• trigonometry
• analytical geometry
• calculus
• modern geometry
• linear and abstract algebra
• history of mathematics
• mathematical investigation
• instrumentation and assessment
• Probability and Statistic

Start Practice Exam Test Questions Part 1 of the Series

Choose the letter of the best answer in each questions.

1. True or false? Consider a random sample of size n from an x distribution. For such a sample, the margin of error for estimating is the magnitude of the difference between x and .

a. False. By definition, the margin of error is the magnitude of the difference between x and .

b. True. By definition, the margin of error is the magnitude of the difference between x and .

c. True. By definition, the margin of error is the magnitude of the difference between x and .

d. False. By definition, the margin of error is the magnitude of the difference between x and .

2. True or false? A larger sample size produces a longer confidence interval for .

a. True. As the sample size increases, the maximal error decreases, resulting in a longer confidence interval.

b. False. As the sample size increases, the maximal error decreases, resulting in a shorter confidence interval.

c. True. As the sample size increases, the maximal error increases, resulting in a longer confidence interval.

d. False. As the sample size increases, the maximal error increases, resulting in a shorter confidence interval.

3. True or false? Every random sample of the same size from a given population will produce exactly the same confidence interval for .

a. True. Different random samples may produce different x values, resulting in different confidence intervals.

b. False. Different random samples may produce different x values, resulting in different confidence intervals.

c. False. Different random samples may produce different x values, resulting in the same confidence intervals.

d. True. Different random samples will produce the same x values, resulting in the same confidence intervals.

4. True or false? If the sample mean of a random sample from an x distribution is relatively small, then the confidence interval for will be relatively short.

a. True. The maximal error of estimate controls the length of the confidence interval depends on the value of x.

b. False. The maximal error of estimate controls the length of the confidence interval regardless of the value of x.

c. True. The maximal error of estimate controls the length of the confidence interval regardless of the value of x.

d. False. The maximal error of estimate controls the length of the confidence interval depends on the value of x.

5. True or false? If the sample mean x of a random sample from an x distribution is relatively small, when the confidence level c is reduced, the confidence interval for becomes shorter.

a. False. As the level of confidence decreases, the maximal error of estimate increases.

b. True. As the level of confidence decreases, the maximal error of estimate decreases.

c. False. As the level of confidence decreases, the maximal error of estimate decreases.

d. True. As the level of confidence decreases, the maximal error of estimate increases.

6. As the degrees of freedom increase, what distribution does the student’s t-distribution become more like?

a. chi-square

b. binomial

c. uniform

d. standard normal

7. What is a null hypothesis?

a. A specific hypothesis where the claim is that the population parameter is equal to 0.

b. Any hypothesis that differs from the original claim being made.

c. A working hypothesis making a claim about the population parameter in question.

d. A specific hypothesis where the claim is that the population parameter does not equal 0.

8. What is an alternate hypothesis?

a. A specific hypothesis where the claim is that the population parameter does not equal 0.

b. A specific hypothesis where the claim is that the population parameter is equal to 0.

c. Any hypothesis that differs from the original claim being made.

d. A working hypothesis making a claim about the population parameter in question.

9. If we fail to reject (i.e., “accept”) the null hypothesis, does this mean that we have proved it to be true beyond all doubt?

a. Yes, if we fail to reject the null, we have found evidence that the null is true beyond all doubt.

b. No, it suggests that the evidence is not sufficient to merit rejecting the null hypothesis.

c. No, it suggests that the null hypothesis is true only some of the time.

d. Yes, it suggests that the evidence is sufficient to merit rejecting the alternative hypothesis beyond all doubt.

10. If we reject the null hypothesis, does this mean that we have proved it to be false beyond all doubt?

a. No, the test was conducted with a risk of a type I error.

b. Yes, if we reject the null that suggests that it is false beyond all doubt.

c. No, the test was conducted with a risk of a type II error.

d. Yes, the test was conducted with a risk of a type I error.

11. Name of the bias that can occur when not everybody from the population is included in the sample?

a. Undercoverage

b. Sampling bias

c. Convenience sampling

d. Response bias

12. What is the difference between descriptive and inferential statistics?

a. Inferential statistics only concerns the sample while descriptive statistics concerns the underlying population

b. Descriptive statistics is used with discrete variables, inferential statistics is used with continuous variables.

c. Inferential statistics is used with discrete variables, descriptive statistics is used with continuous variables.

d. Descriptive statistics only concerns the sample, inferential statistics concerns the underlying population.

13. What is the central limit theorem?

a. It says that the sampling distribution forms a bell shape given that the sample is large enough and the population distribution is bell-shaped.

b. It says that the mean is centered if the sample size is infinity.

c. It says that the sampling distribution forms a bell shape given that the sample is large enough.

d. It says that the population distribution approximates a bell shape given that the sample is large enough.

14. What can you say if a sample distribution (very large sample size) is very different from the population distribution?

a. You have to do further research

b. The sample is biased and does not represent the population well

c. No issues and may proceed with the analysis

d. Population is biased

15. Suppose you would like to estimate the proportion of the satisfied customer. Which of the following would be the best point estimate to use?

a. The number of satisfied customers out of a random sample of 100 customers.

b. The proportion of satisfied customers out of a random sample of 100 customers.

c. The proportion of satisfied customers out of the latest 100 customers to contact customer services.

d. The average customer satisfaction rating given by a random sample of 100 customers.

16. You received several complaints that a specific type of doll you sell, the DollX, is defective. You decided to test 5 out of the 50 DollX chains you have in stock to determine whether or not you should report the fault to the supplier. What is the population of interest in this study?

a. All dolls

b. All previously sold DollX

c. All DollX

d. The 5 selected DollX

17. You received several complaints that a specific type of doll you sell, the DollX, is defective. You decided to test 5 out of the 50 DollX chains you have in stock to determine whether or not you should report the fault to the supplier. What is the sample of interest in this study?

a. All dolls

b. All previously sold DollX

c. All DollX

d. The 5 selected DollX

18. Which of the statement(s) is/are correct?

I. A disadvantage of a telephone interview compared to a face-to-face questionnaire is that people tend to be less patient.

II. The cheapest way of collecting data is an online survey.

a. Statement II is correct, statement I is incorrect.

b. Statement I is correct, statement II is incorrect.

c. Both statements are incorrect.

d. Both statements are correct.

19. Do the probabilities add up to 1? Should they add up to 1?

a. Yes, but they should not because these values do not cover the entire sample space.

b. Yes, because these values cover the entire sample space.

c. No, because these values do not cover the entire sample space.

d. No, but they should because these values cover the entire sample space.

20. A sample space must be collectively exhaustive and mutually exclusive.

a. true

b. false

c. either

d. neither

21. Discrete random variables arise from measurement.

a. true

b. false

c. either

d. neither

22. Which of the following is a continuous variable?

a. number of traffic fatalities per year in the state of Florida

b. number of ships in Pearl Harbor on any given day

c. time required to drive from home to college on any given day

d. number of days someone lives

23. What does it mean to say that the trials of an experiment are independent?

a. One outcome is less likely to happen than the other outcomes

b. The outcome of one trial affects the probability of success on any other trial.

c. The outcome of one trial does not affect the probability of success on any other trial.

d. One outcome is more likely to happen than the other outcomes.

24. Which of the following is not a continuous variable?

a. time to solve a problem

b. temperature

c. height

d. number of children in a family

25. Real limits are important whenever you are measuring a(n) _____ variable.

a. independent

b. dependent

c. discrete

d. continuous

26. What does a standard score measure?

a. the number of standard deviations a measurement is from the mean

b. the number of standard deviations a measurement is from the lowest value

c. the number of standard deviations a measurement is from the highest value

d. the number of standard deviations that are present under a normal curve

27. Does a raw score less than the mean correspond to a positive or negative standard score? What about a raw score greater than the mean?

a. Raw scores less than the mean will have negative standard scores; raw scores above the mean will have positive standard scores.

b. Raw scores less than the mean will have positive standard scores; raw scores above the mean will have negative standard scores.

c. Raw scores below and above the mean will have negative standard scores.

d. Raw scores below and above the mean will have positive standard scores.

28. If car insurance rates for teenagers is approximately normally distributed with a standard deviation of $620 per year, find the mean insurance rate for teenagers if 10.56% of teenagers pay more than $3,000 annually for car insurance.

a. $2,225

b. $3,775

c. $2,935

d. $2,380

29. Normal distribution can have a mean that corresponds to a negative number.

a. true

b. false

c. sometimes

d. neither

30. A z-score of z = −2.00 indicates a position in a distribution __________.

a. below the mean by 2 points

b. above the mean by a distance equal to 2 standard deviations

c. below the mean by a distance equal to 2 standard deviations

d. above the mean by 2 points

31. For a distribution of scores, which of the following z-score values represents the location closest to the mean?

a. z = -2.00

b. z = -1.00

c. z = +0.50

d. z = +1.00

32. For a population with =80 and =12, what is the z score corresponding to X=92?

a. z = +12.00

b. z = +1.20

c. z = +1.00

d. z = +0.50

33. For the past 20 years, the high temperature on April 15th has averaged =62 degrees with a standard deviation of =4. Last year, the high temperature was 72 degrees. Based on this information, which of the following best describes last year’s temperature on April 15th?

a. There is not enough information to compare last year with the average.

b. Above average, but it is impossible to describe how much above average

c. Far above average

d. A little above average

34. If two events are mutually exclusive, can they occur concurrently?

a. Yes. By definition, mutually exclusive events can occur together.

b. No. By definition, mutually exclusive events cannot occur together.

c. No. Two events will never occur concurrently.

d. Yes. Any two events can occur concurrently.

35. For a normal distribution, is it likely that a data value selected at random is more than 2 standard deviations above the mean?

a. No. This event happens only 16% of the time.

b. No. This event happens only .015% of the time.

c. No. This event happens only 2.5% of the time.

d. Yes. This event happens quite frequently.

36. On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5. If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss?

a. Yes, since the coin is fair.

b. No, each outcome is equally likely regardless of the previous outcome.

c. Yes, tails will always result on the second toss.

d. No, tails will never occur on the second toss.

37. Consider a Statistics class with 45 female students and 55 male students. Only 25 females passed a difficult midterm exam, whereas 30 males passed the same exam. What is the probability that a randomly chosen student passed the exam?

a. 55%

b. 25/45

c. 45%

d. 1/4

38. Consider the probability distribution of a random variable x. Is the expected value of the distribution necessarily one of the possible values of x?

a. No. The expected value can be a value different from the exact value of x.

b. Yes. The expected value must always be one of its possible values of x.

c. Yes. The expected value can never be a value from the exact value of x.

d. No. The expected value will never be one of its possible values of x.

39. What does the random variable for a binomial experiment of n trials measure?

a. The random variable measures the standard deviation of n trials.

b. The random variable measures the number of failures out of n trials.

c. The random variable measures the number of successes out of n trials.

d. The random variable measures the mean of n trials.

40. Consider two normal curves. If the first one has a larger mean than the second one, must it have a larger standard deviation as well?

a. No. The values of and are independent.

b. Yes. The values of and are independent.

c. No. As increases, will decrease.

d. Yes. As increases, must also increase.

41. Raul received a score of 78 on a history test for which the class mean was 70 with a standard deviation of 8. He received a score of 74 on a biology test for which the class mean was 70 with a standard deviation of 4. On which test did he do better relative to the rest of the class?

a. biology test

b. history test

c. the same

d. none

42. Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 6.0 minutes and a standard deviation of 1.5 minutes. For a randomly received emergency call, find the probability that the response time is between 3 and 7 minutes.

a. 0.2525

b. 0.0228

c. 0.7248

d. none

43. Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 58 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean =58 tons and standard deviation = ton. Suppose the weight of coal in 45 cars selected at random had an average x of less than 57.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

a. Yes, the probability that this deviation is random is very small.

b. Yes, the probability that this deviation is random is very large.

c. No, the probability that this deviation is random is very small.

d. No, the probability that this deviation is random is very large.

44. Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean =7100 and estimated standard deviation = 850. A test result of x<3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. What is the probability that, on a single test, x is less than 3500?

a. 0.1033

b. 0.1133

c. 0.1233

d. 0.1333

45. One of the top paid female wrestlers is 28 years old. If her age is 0.55 standard deviations below the mean, and the standard deviation for female wrestler ages is 5.9 years, what is the average age for all female wrestlers? Assume that female wrestler ages can be modeled with a normal distribution.

a. not enough information is given

b. 31.2

c. 23.3

d. 24.8

46. Consider a family with 4 children. Assume the probability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5, and that the events “boy” and “girl” are independent. What is the probability that all 4 children are male?

a. 1/16

b. 2/16

c. 3/16

d. 4/16

47. You flip a fair coin (i.e., the probability of obtaining Heads is 1/2) three times. Assume that all sequences of coin flip results, of length 3, are equally likely. Determine the probability of any sequence in which the number of Heads is greater than or equal to the number of Tails.

a. 1/2

b. 1/4

c. 3/8

d. 3/16

48. Consider two discrete probability distributions with the same sample space and the same expected value. Are the standard deviations of the two distributions necessarily equal?

a. No, the individual probabilities may differ in a way that produces the same expected value but a different standard deviation.

b. No, the standard deviations of two different discrete probability distributions are never equal.

c. Yes, because both distributions have the same expected value, they will have the same standard deviation as well.

d. Yes, because both distributions have the same sample space, they will have the same standard deviation as well.

49. In an experiment, there are n independent trials. For each trial, there are three outcomes, A, B, and C. For each trial, the probability of outcome A is 0.50; the probability of outcome B is 0.20; and the probability of outcome C is 0.30. Suppose there are 10 trials. Can we use the binomial experiment model to determine the probability of four outcomes of type A, five of type B, and one of type C?

a. Yes. Each outcome has a probability of success and failure.

b. Yes. A binomial probability model applies to three outcomes per trial.

c. No. A binomial probability model applies to only one outcome per trial.

d. No. A binomial probability model applies to only two outcomes per trial.

50. Consider the following scores. (i) a score of 40 from a distribution with a mean of 50 and standard deviation 10 (ii) a score of 45 from a distribution with a mean of 50 and standard deviation 5. How do the two scores compare relative to their respective distributions?

a. They are both 1 standard deviation below their respective means.

b. They are both 2 standard deviations below their respective means.

c. They are both 1 standard deviation above their respective means.

d. The score of 40 is 2 standard deviations below its mean, while the score of 45 is only 1 standard deviation below its mean.

LET REVIEW MATERIALS