# 25 mcqs in statistics …

1. The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 15.0 pounds, and the standard deviation of the normally distributed weights is 1.75 pounds. Of the 200 plants in the experiment, how many produced peppers weighing between 13 and 16 pounds?

Answer

100

118

197

53

2. Which of the following is true in a normal distribution?

Answer

Mean equals the mode and the median

Mode equals the median

Mean divides the distribution into two equal parts

All of the above are correct

3. A z-score is the distance between a selected value (X) and the population mean (µ) divided by the population standard deviation (σ).

Answer

True

False

4. A study of a company’s practice regarding the payment of invoices revealed that an invoice was paid an average of 20 days after it was received. The standard deviation equaled five days. Assuming that the distribution is normal, what percent of the invoices were paid within 15 days of receipt?

15.87%

37.91%

34.13%

86.74%

5. The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, what test score separates the top 5% of the students from the lower 95% of students?

Answer

81.48

90.00

83.72

78.96

6. The shape of any uniform probability distribution is

Answer

Negatively skewed

Positively skewed

Rectangular

Bell shaped

7. Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Tests revealed that the tire’s mileage is normally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 5 percent of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce?

Answer

44,528

32,960

49,621

40,922

8. The mean amount of gasoline and services charged by Key Refining Company credit customers is \$70 per month. The distribution of amounts spent is approximately normal with a standard deviation of \$10. What is the probability of selecting a credit card customer at random and finding the customer charged between \$70 and \$83?

Answer

0.1962

0.4032

0.3413

0.4750

9. In stratified random sampling, a population is divided into subgroups called strata and a sample is randomly selected from each stratum.

Answer

True

False

10 . 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 that a sample mean would exceed 20 hours per week?

Answer

1.0

0.5

1.96

Cannot be calculated based on the given information.

11. When systematic random sampling is used, the central limit theorem cannot be applied.

Answer

True

False

12. The standard error of the mean will vary according to the size of the sample. As the sample size n gets larger, the variability of the sample means gets smaller.

Answer

True

False

13. Based on the central limit theorem, sampling error will decrease as sample size decreases.

Answer

True

False

14. 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?

Answer

0.0228

0.9772

0.4772

0.9544

15. A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women, 18-21 years of age, a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September.

Answer

The sample size was 4.

The sample size was 100.

The sample size was 400.

The sample size was 1.

16. Based on the central limit theorem, the mean of all the sample means is

Answer

X

µ

σ

α

17. A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.

Given the probability distribution, which of the following predictions is correct?

Number of absent Probability

0 0.6

1 0.2

2 0.12

3 0.04

4 0.04

5 0

Answer

60% of the employees will have more than one day absent   for a month.

There   is a 0.04 probability that an employee will be absent 1 day during a month.

There is a 0.12 probability that an employee will be   absent 2 days during a month.

There is a 0.50 probability that an employee will be   absent 0.72 days during a month.

18.

A binomial distribution is a continuous probability distribution.

Answer

True

False

19. David’s gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period twenty-five customers buy gasoline at this station.

This situation is an example of what type of discrete probability distribution?

Answer

Continuous probability distribution

Poisson probability distribution

Binomial probability distribution

Hypergeometric probability distribution

20. The weight of an offensive linesman may be 205.15 pounds, 210.23 pounds, 225.05 pounds or 219.14 pounds. What is this an illustration of?

Answer

Continuous random variable

Discrete random variable

Complement rule

All of the above

21. Sixty percent of the customers of a fast food chain order a hamburger, french fries and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?

Answer

1.000

0.186

0.403

0.000

22. To construct a binomial probability distribution, the number of trials and the probability of success must be known.

Answer

True

False

23. The probability of a particular outcome must always be between 0 and 100 inclusive.

Answer

True

False

24. The binomial probability distribution is always negatively skewed.

Answer

True

False

25 . A discrete random variable can have only certain clearly separated values.

Answer

True

False