25 mcqs in statistics …


1. Which of the following is correct about a probability distribution?



Sum of all possible outcomes must equal 1


Outcomes must be mutually exclusive


Probability of each outcome must be between 0   and 1 inclusive


All of the above


For the following distribution

x P(x)

0 0.13

1 0.346

2 0.346

3 0.154

4 0.026

what is the mean distribution

A: 1

B: 2.5

C: 1.604

D: 3 


A machine shop has 100 drill presses and other machines in constant use. The probability that a machine will become inoperative during a given day is 0.002. During some days no machines are inoperative, but during some days, one, two, three or more are broken down. What is the probability that fewer than two machines will be inoperative during a particular day?










4. A new car was put into production. It involved many assembly tasks. Each car was inspected at the end of the assembly line and the number of defects per unit was recorded. For the first 100 cars produced, there were 40 defective cars. Some of the cars had no defects; a few had one defect, and so on. The distribution of defects followed a Poisson distribution. Based on the first 100 produced, about how many out of every 1,000 cars assembled should have one or more defects?



About 660


About 165


About 630


About 330

5. What is the only variable in the Poisson probability formula?










6. For a binomial distribution, the probability of a success stays the same for each trial, but the probability of a failure varies from trial to trial.


7. The variance of a binomial distribution is found by η π (1 – π).


8. What kind of distribution are the binomial and Poisson distributions?







Both discrete and continuous


Neither discrete or continuous

9. To construct a binomial distribution, it is necessary to know the total number of trials and the probability of success on each trial.


10. Which of the following is NOT true regarding the normal distribution?



Mean, median and mode are all equal


It has a single peak


It is symmetrical


The points of the curve meet the X-axis at z = -3 and z = 3

11. Ball-Bearings, Inc. produces ball bearings automatically on a Kronar BBX machine. For one of the ball bearings, the mean diameter is set at 20.00 mm (millimeters). The standard deviation of the production over a long period of time was computed to be 0.150 mm. What percent of the ball bearings will have diameters 20.27 mm or more?










12. The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, what is the probability that a student scored greater than 65?










13. An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before they failed is 19.0 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.2 hours. About 95.44 percent of the batteries failed between what two values?



8.9 and 18.9


12.2 and 14.2


14.1 and 22.1


16.6 and 21.4

14. A large manufacturing firm tests job applicants who recently graduated from college. The test scores are normally distributed with a mean of 500 and a standard deviation of 50. Management is considering placing a new hire in an upper level management position if the person scores in the upper 6 percent of the distribution. What is the lowest score a college graduate must earn to qualify for a responsible position?










15. The uniform probability distribution is symmetric about the mean and median.


16. The z-scores for X values greater than the mean are negative.


17. Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5 percent of production based on past experience. Past records indicate that, on the average, 4,000 units of a small assembly are produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. If the bonus is paid on the upper 5 percent of production, the bonus will be paid on how many units or more?










18. If 40 samples of size 21 were selected from a population of 22,493, we would expect the mean of the sample means and the population mean to be close but not exactly equal.


19. Suppose we select every fifth invoice in a file. What type of sampling is this?










20. An accounting firm is planning for the next tax preparation season. From last year’s returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the average time to complete a tax form?



The population distribution is skewed to the   right.


The population distribution is skewed to the   left.


The population distribution is normal.


The shape of the population distribution does not matter.

21. An accounting firm is planning for the next tax preparation season. From last year’s returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the probability that the mean completion time will be more than 120 minutes?



Approximately zero







22. The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a person would score 130 or more on the test?










23. We can expect some difference between sample statistics and the corresponding population parameters. This difference is called the sampling error.


24. What sample statistic is used to estimate a population parameter?





Sampling error


Point estimate


Interval estimate

25. A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the probability of finding a sample mean less than 18 hours?










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