# Math final exam

1. The mean amount spent by a family of four on food is $500 per month with a standard deviation of $75. Assuming that the food costs are normally distributed, what is the probability that a family spends less than $410 per month?

0.1151

0.0362

0.8750

0.2158

2. As the size of the sample increases, what happens to the shape of the distribution of sample means?

It cannot be predicted in advance.

It is negatively skewed.

It approaches a normal distribution.

It is positively skewed.

3. What is the following table called?

Ages

Number of Ages

20 up to 30

16

30 up to 40

25

40 up to 50

51

50 up to 60

80

60 up to 70

20

70 up to 80

8

Frequency polygon

Frequency distribution

Histogram

Cumulative frequency distribution

4. How is the t distribution similar to the standard z distribution?

Both are continuous distributions.

Both are skewed distributions.

Both are families of distributions.

Both are discrete distributions.

5. In a distribution, the second quartile corresponds with the __________.

Median

Variance

Mean

Mode

6. A random sample of 85 supervisors revealed that they worked an average of 6.5 years before being promoted. The population standard deviation was 1.7 years. Using the 0.95 degree of confidence, what is the confidence interval for the population mean?

6.99 and 7.99

6.14 and 6.86

4.15 and 7.15

6.49 and 7.49

x±z(S/ Ön)

7. Incomes of 50 loan applicants are obtained. Which level of measurement is income?

Ordinal

Nominal

Ratio

Interval

8. Which of the following is an example of a continuous variable?

Zip codes of shoppers.

Number of students in a statistics class.

Tons of concrete to complete a parking garage.

Rankings of baseball teams in a league.

9. For the normal distribution, the mean plus and minus two standard deviations will include about what percent of the observations?

99.7%

68%

50%

95%

10. The main purpose of descriptive statistics is to:

Summarize data in a useful and informative manner.

Determine if the data adequately represents the population.

Make inferences about a population.

Gather or collect data.

11. Which of the following is true regarding the normal distribution?

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

It is asymmetrical.

It has two modes.

The mean, median, and mode are all equal.

12. What is the relationship among the mean, median, and mode in a symmetric distribution?

The mean is always the smallest value.

They are all equal.

The mean is always the largest value.

The mode is the largest value.

13. The probability distribution for the number of automobiles lined up at a Lakeside Olds dealer at opening time (7:30 a.m.) for service is:

Number

Probability

1

0.05

2

0.30

3

0.40

4

.25

On a typical day how many automobiles should Lakeside Olds expect to be lined up at opening time? Use expected value or mean of the probability distribution.

2.85

1.00

10.00

1.96

14. Which of the following is a point estimate for the population mean (µ)?

X”

x/n

s

σ

15. When all the items in a population have an equal chance of being selected for a sample the process is called _________________.

Simple random sampling

Z-score

Non-probability sampling

Sampling error

16. A student was interested in the cigarette smoking habits of college students and collected data from an unbiased random sample of students. The data is summarized in the following table:

Males who smoke

20

Males who do not smoke

30

Females who smoke

25

Females who do not smoke

50

What type of chart best represents relative class frequencies?

Pie chart

Scatter plot

Frequency polygon

Box plot

17. A listing of all possible outcomes of an experiment and their corresponding probabilities of occurrence is called a ____________.

Probability distribution

Random variable

Frequency distribution

Subjective probability

18. The distribution of a sample of the outside diameters of PVC pipes approximates a symmetrical bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68% of the outside diameters lie between what two amounts?

13.8 and 14.2 inches

13.5 and 14.5 inches

13.9 and 14.1 inches

13.0 and 15.0 inches

19. For the past week a company’s common stock closed with the following prices: $61.5, $62, $61.25, $60.875, and $61.5. What was the price range?

$1.750

$1.875

$1.250

$1.125

20. Judging from recent experience 5% of the computer keyboards produced by an automatic high-speed machine are defective. If six keyboards are randomly selected, what is the probability that none of the keyboards are defective? Use binomial distribution.

0.500

0.001

0.735

0.167

21. The National Center for Health Statistics reported that of every 883 deaths in recent years, 24 resulted from an automobile accident, 182 from cancer, and 333 from heart disease. What is the probability that a particular death is due to an automobile accident?

539/883 or 0.610

182/883 or 0.206

24/333 or 0.072

24/883 or 0.027

22. The mean of a normal probability distribution is 500 and the standard deviation is 10. About 95% of the observations lie between what two values?

350 and 650

475 and 525

400 and 600

480 and 520

23. Which of the following is a characteristic of the normal probability distribution?

It’s bell-shaped.

It’s asymmetrical.

It’s rectangular.

It’s positively skewed.

24. Refer to the following breakdown of responses to a survey of “Are you concerned about being tracked while connected to the Internet?”

Response

Frequency

Very concerned

140

Somewhat concerned

40

No concern

20

What is the class with the greatest frequency?

Very concerned

No concern

None apply

Somewhat concerned

25. The names of the positions in a corporation such as chief operating officer or controller are examples of what type of variable?

Interval

Ratio

Quantitative

Qualitative

26. The members of each basketball team wear numbers on their jerseys. What scale of measurement are these numbers considered?

Interval

Nominal

Ratio

Ordinal

27. A portion or part of a population is called a:

Random survey

Frequency distribution

Sample

Tally

28. Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The results showed that the mean tread life was 50,000 miles, with a standard deviation of 3,500 miles. What is the best estimate of the mean tread life in miles for the entire population of these tires?

3,500

500

35

50,000

29. A large manufacturing firm tests job applicants. 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 sixth percent of the distribution. What is the lowest score a new hire must earn to qualify for a responsible position?

625

50

460

578

30. The following graph is a:

Box plot

Contingency table

Dot plot

Stem-and-leaf display

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