The following problems are currently ( Fall 2003 ) not covered on the Math 210 Final :
#34,  42,  51
 This is in no way all of the information that you should know for the FINAL.

FINAL REVIEW PROBLEMS

(1) According to the above histogram on the heights of active volcanoes, how many volcanoes are less than 3500 feet tall?
(a) 5
(b) 8
(c) 10
(d) 12
(e) 15

(2) What is the missing frequency in the following frequency distribution?

Class

Frequency

Cumulative Frequency

0-9

5

5

10-19

12

17

20-29

?

32

30-39

8

40

(a) 15
(b) 17
(c) 20
(d) 25
(e) 32

(3) For the data 5, 9, 2, 11, 7, 19, and 8, what is the range?
(a) 3
(b) 7
(c) 11
(d) 17
(e) 19

(4) What is the mode of the following data set: 2, 1, 3, 2, 1, 0, 4, 3, 2, 3, 4, 2, 1, 3, 2?
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4

(5) A distribution has a mean of 200 and a standard deviation of 30. For a data value of 245, what is the z-score?
(a) -1.50
(b) -1.20
(c) 1.20
(d) 1.50
(e) 1.75

(6) The value with 25% of the data observations below it is the
(a) median
(b) first quartile (Q1)
(c) third quartile (Q3)
(d) mode
(e) interquartile range

(7) Find the sample variance of the following data: 60, 72, 85, 89, 92, 54, 75, 81, 97.
(a) 13.66
(b) 14.49
(c) 17
(d) 186.67
(e) 210.00

(8) A teenager has 8 tee shirts, 2 belts, and 5 pairs of jeans. How many different outfits can he wear, assuming he always wears a belt?
(a) 15
(b) 16
(c) 21
(d) 40
(e) 80

(9) A florist can select 5 different flowers for a bouquet from a selection of 12 different types. How many different sets of flowers can be chosen for the bouquet?
(a) 17
(b) 60
(c) 120
(d) 792
(e) 95040

(10) A photographer wishes to choose 4 photos from a selection of 8 photos to display in a row on a wall. How many different arrangements of photos can he choose from?
(a) 4
(b) 8
(c) 32
(d) 70
(e) 1680

(11) A box contains 5 red, 2 white, and 3 green marbles. If a marble is selected from the box at random, find the probability that it is red or white.
(a) 0.2
(b) 0.3
(c) 0.5
(d) 0.7
(e) 0.8

(12) The probability of a California teenager owning a surfboard is 0.43, of owning a skateboard is 0.38, and of owning both is 0.28. If a California teenager is selected at random, find the probability that he or she owns a surfboard or a skateboard.
(a) 0.81
(b) 0.05
(c) 0.16
(d) 0.10
(e) 0.53

USE THE FOLLOWING INFORMATION TO ANSWER QUESTIONS 13 & 14.
A store sells 3 types of appliances in 3 colors. The following table lists the number of items of each type in stock.

 

White

Almond

Black

Refrigerator

12

10

3

Washer

10

8

5

Dryer

11

11

4

(13) If an item is selected at random, what is the probability that it is not black?
(a) 6/37
(b) 31/37
(c) 33/74
(d) 29/74
(e) 25/74

(14) Given that an appliance is white, what is the probability that it is a refrigerator?
(a) 12/33
(b) 12/25
(c) 6/37
(d) 33/74
(e) 25/74

USE THE FOLLOWING INFORMATION TO ANSWER QUESTIONS 15, 16, & 17
The probability distribution of the number of cartoons watched by first graders on Saturday mornings is shown in the following table.

x

0

1

2

3

4

5

P(x)

0.2

0.2

0.3

0.15

0.1

0.05

(15) What is the mean of this distribution?
(a) 1.9
(b) 2.0
(c) 2.4
(d) 2.6
(e) 3.1

(16) What is the standard deviation of this distribution?
(a) 0.34
(b) 1.41
(c) 1.99
(d) 2.37
(e) 5.6

(17) What is the probability that a randomly selected child watches fewer than 3 cartoons?
(a) 0.15
(b) 0.30
(c) 0.45
(d) 0.70
(e) 0.85

(18) If we have a binomial distribution with n = 200 and p = 0.47, what is the variance of this distribution?
(a) 106
(b) 94
(c) 49.82
(d) 44.18
(e) 7.06

(19) If we have a binomial distribution with n = 5 and p = 0.35, what is the P(X=2)?
(a) 0.0336
(b) 0.1225
(c) 0.3364
(d) 0.70
(e) 1.75

(20) If approximately 32% of adults cut their sandwiches in half before eating them, find the probability that in a group of 9 adults, exactly 4 cut the sandwich in half before eating it.
(a) 0.0015
(b) 0.0034
(c) 0.0105
(d) 0.1921
(e) 0.2681

(21) Scores on a statewide proficiency test are normally distributed with mean 68.2 and standard deviation 14.6. The state would like to identify the 10% of students with the lowest scores for remedial work. What is the cutoff score for students needing remedial work?
(a) .0398
(b) 1.28
(c) 64.55
(d) 71.85
(e) 49.51

(22) The average hourly wage of workers at a fast food restaurant is $5.85 with standard deviation $0.35. Assume that the distribution is normally distributed. If a worker at this restaurant is selected at random, find the probability that the worker earns more than $6.50 per hour.
(a) 0.4686
(b) 0.0314
(c) 0.0322
(d) 0.9686
(e) 0.4678

(23) The average repair cost for automatic washers is $73 with a standard deviation of $8. The costs are normally distributed. If 9 washers are repaired find the probability that the mean of the repair bills will be less than $69.50.
(a) 0.1700
(b) 0.3300
(c) 0.4049
(d) 0.0951
(e) 0.0001

(24) A medical researcher is investigating the pulse rates of smokers (population 1) and the pulse rates of nonsmokers (population 2). A sample of 100 smokers had a mean of 90 and a standard deviation of 5. A sample of 100 nonsmokers had a mean of 88 and a standard deviation of 6. What are the null and alternative hypotheses that would be used to determine if the smokers have higher pulse rates than the nonsmokers?
(a) H0: m1 - m2 ³ 0 vs. Ha: m1 - m2 < 0
(b) H0: s 12/s 22 £ 1 vs. Ha: s 12/s 22 > 1
(c) H0: m1 - m2 = 0 vs. Ha: m1 - m2 (not =) 0
(d) H0: s 12/s 22 ³ 1 vs. Ha: s 12/s 22 < 1
(e) H0: m1 - m2 £ 0 vs. Ha: m1 - m2 > 0

(25) In 1993, 3% of elementary schools did not have computers. In a sample of 180 elementary schools, find the probability that 6 or fewer did not have computers.
(a) 0.3156
(b) 0.5832
(c) 0.7031
(d) 0.5160
(e) 0.0001

(26) A sample of 36 job seekers took an average of 5.9 months to find a new job. If the population standard deviation is 0.8 months, find the 95% confidence interval for the mean.
(a) (5.64, 6.16)
(b) (5.68, 6.12)
(c) (5.86, 5.94)
(d) (5.56, 6.24)
(e) (5.48, 6.32)

(27) A tourism group wishes to estimate the average cost of a lobster dinner for their city within $0.50 with 95% confidence. It is known that the standard deviation of prices is $2.25. How large of a sample size should the group take?
(a) 1
(b) 9
(c) 78
(d) 88
(e) 7780

(28) Find the appropriate critical value to use in a 99% confidence interval for the mean when s is unknown and the sample size is 18?
(a) 2.58
(b) 2.88
(c) 2.90
(d) 1.96
(e) 1.65

(29) A survey of 80 families showed that 36 of them had at least two TV sets at home. Find the 90% confidence interval for the proportion of families with at least two TV sets.
(a) (29.76, 42.24)
(b) (0.364, 0.536)
(c) (0.359, 0.541)
(d) (0.445, 0.455)
(e) (0.407, 0.493)

(30) A pharmaceutical company wishes to market a new product to consumers over the age of 50. They plan to advertise on a certain TV show if the average age of the viewer is over 50. What hypotheses should the company test?
(a) H0: m ³ 50 vs. Ha: m < 50
(b) H0: m £ 50 vs. Ha: m > 50
(c) H0: m=50 vs. Ha: m (not =) 50
(d) H0: ³ 50 vs. Ha: < 50
(e) H0: £ 50 vs. Ha: > 50

USE THE FOLLOWING MINITAB OUTPUT TO ANSWER QUESTIONS #31 AND #32

Minitab was used to obtain a fitted line plot that relates the number of years of experience and the current annual income (in thousands) for a random sample of blue collar workers.
Regression
The regression equation is y = 11.0 + 2.66 x

Predictor

Coef

StDev

T

P

Constant

11.031

2.050

5.38

0.000

x

2.6563

0.5870

4.52

0.000

S = 3.321 R-Sq = 71.9% R-Sq(adj) = 68.4%

(31) If a randomly selected worker has 5 years of experience, what is his expected annual salary.
(a) 24300
(b) 18000
(c) 20000
(d) 21640
(e) 26960

(32) What is the coefficient of correlation (r) for the data used in the regression problem.
(a) -0.827
(b) -0.719
(c) -0.848
(d) 0.719
(e) 0.848

(33) Minitab was used to conduct a test of hypothesis. What is the P-value for this test?
Z-Test
Test of mu = 14.000 vs mu not = 14.000
The assumed sigma = 3.00

Variable

N

Mean

StDev

SE Mean

Z

P

C1

30

14.647

2.726

0.548

1.18

 

(a) 0.1190
(b) 0.2380
(c) 0.3643
(d) 0.3810
(e) 0.7620

(34) Minitab was used to conduct a test of hypothesis. What is the P-value for this test?
T-Test of the Mean
Test of mu = 10.000 vs mu < 10.000

Variable

N

Mean

StDev

SE Mean

T

P

C1

26

8.718

3.042

0.585

-2.19

 

(a) P-value = 0.0143
(b) P-value = 0.019
(c) P-value = 0.038
(d) P-value = -0.0143
(e) P-value = 0.0286

(35) Minitab was used to conduct a test of hypotheses for two samples. Based on this partial Minitab output, what conclusion should be reached for the test when using a 0.05 level of significance?
Two Sample T-Test and Confidence Interval
Two sample T for C1 vs C2

 

N

Mean

StDev

SE Mean

C1

27

8.72

3.04

0.59

C2

27

9.84

2.86

0.55

95% CI for mu C1 - mu C2: ( -2.73, 0.49)
T-Test mu C1 = mu C2 (vs not =): T= P=0.17 DF=
(a) Reject Ho
(b) Do Not Reject Ho
(c) There is not enough information given in the problem to make a decision.

(36) A random sample of 81 students at a local university showed that they work an average of 100 hours per month with a population standard deviation of 27 hours. Compute a 95% confidence interval for the mean of the population.
(a) (94.03 , 105.97)
(b) (94.12 , 105.88)
(c) (95.07 , 104.94)
(d) (95.01 , 104.99)
(e) (93.02 , 106.98)

(37) It is known that the variance of the population equals 484. With a 0.90 probability, how large of a sample would have to be taken to provide a sampling error of 3 or less?
(a) n=89
(b) n=146
(c) n=207
(d) n=70434
(e) n=99991

(38) A large corporation wants to determine whether the average age of their employees is significantly more than 40. A sample of 20 employees is selected. The average age in the sample was 45 years with a sample standard deviation of 5 years. Assuming the distribution of the population is normal, what is the value of the test statistic that would be used to determine if the mean age of the employees is significantly more than 40 years?
(a) -4.47
(b) -0.22
(c) 0
(d) 0.22
(e) 4.47

(39) The manager of the quality control department at MNM Corporation, a producer of various kinds of batteries, has said that their "D" size batteries last more than 87 hours. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours. In order to support his claim, the manager conducts a test of hypothesis and gets 1 for the value of the test statistic. What conclusion should the manager make if he uses a 0.05 level of significance?
(a) Reject Ho
(b) Do Not Reject Ho
(c) There is not enough information given in the problem to make a decision.

(40) In the last presidential election, a national survey company claimed that more than 50% of all registered voters voted for the Democratic candidate. In a random sample of 400 registered voters, 208 voted for the Democratic candidate. What is the null and alternative hypotheses that would be used to determine if more than 50% voted Democratic?
(a) Ho: p ³ .52 versus Ha: p < .52
(b) Ho: p = .52 versus Ha: p (not =) .52
(c) Ho: p = .50 versus Ha: p (not =) .50
(d) Ho: p £ .50 versus Ha: p > .50
(e) Ho: p ³ .50 versus Ha: p < .50

(41) An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 months was taken. The results of the sample are presented below. What is the slope of the least squares regression line?

Interest Rate (in percent) X

9.2

7.6

10.4

5.3

Monthly Sales Y

22

20

10

45

(a) -1.39
(b) 6.25
(c) -6.25
(d) 1.39
(e) 75.1

(42) Two new processing methods are tested at a factory. It is hypothesized that there is no difference in the variances of the time needed to process products. A sample of 11 products using Process A show a variance of 4.5 minutes and a sample of 8 products using process B show a variance of 5.2 minutes. Using a 0.05 level of significance, we want to determine if there is a difference in the variances of the two processes. If we use the test statistic F = 5.2/4.5 = 1.56 , what is the appropriate rejection region?
(a) Reject Ho if F > 3.14
(b) Reject Ho if F > 3.14 or F < 0.275
(c) Reject Ho if F > 4.76 or F < 0.253
(d) Reject Ho if F > 3.95 or F < 0.210
(e) Reject Ho if F > 3.51 or F < 0.238

(43) A study of corporate business costs was conducted to determine if there was a difference between the average amount spent on dinner by executives and the average amount spent on dinner by managers. What is the value of the test statistic in this test of hypothesis?

 

Executives

Managers

Sample Mean

25.50

22.50

Sample Standard Deviation

4.75

2.83

Sample Size

32

35

(a) 1.960
(b) 3.172
(c) 6.338
(d) 3.104
(e) 6.265

(44) In a wage discrimination case involving male and female employees, independent samples of male and female employees with 5 years or more experience provided the following hourly wage results. We wish to conduct a test of hypothesis using a 0.05 level of significance in order to determine if the average hourly wage of the male workers is exceeds the average hourly wage of the female workers. What are the appropriate degrees of freedom for this test?

 

Male

Female

Sample Mean

$9.25

$8.70

Sample Standard Deviation

$1.00

$0.80

Sample Size

21

19

(a) 20
(b) 38
(c) 19
(d) 21
(e) 18

(45) Independent random samples selected from two normal populations produced the following results.

 

Sample 1

Sample 2

Sample Mean

5.4

4.9

Sample Standard Deviation

3.4

4.8

Sample Size

17

12

We wish to conduct a test of hypothesis to determine if the population means of these two samples are different. Using a 0.05 level of significance, what is the appropriate critical region for this test?
(a) Reject Ho if t > 1.960 or t < -1.960
(b) Reject Ho if t > 1.796 or t < -1.796
(c) Reject Ho if t > 2.052 or t < -2.052
(d) Reject Ho if t > 2.201 or t < -2.201
(e) Reject Ho if t > 2.228 or t < -2.228

(46) An urn contains 6 green balls, 5 white balls, and 3 brown balls. A ball is selected, its colored noted, and then it is replaced. When two balls are selected in this manner, what is the probability that both balls are brown?
(a) 0.0306
(b) 0.0329
(c) 0.0459
(d) 0.0495
(e) 0.2143

(47) A box contains 9 red, 5 yellow, and 4 blue marbles. A marble is drawn, it is not replaced, and a second marble is drawn. What is the probability that both of the marbles are yellow?
(a) 0.0617
(b) 0.0654
(c) 0.0772
(d) 0.0865
(e) 0.2778

(48) A recent study shows that babies who weigh less than 5.5 pounds at birth have a 40% chance to develop high blood pressure as adults. If 12 babies who weighed less than 5.5 pounds at birth are selected at random, what is the probability that at most two of these babies will develop high blood pressure as adults?
(a) 0.020
(b) 0.064
(c) 0.083
(d) 0.917
(e) 0.980

(49) A purchasing agent has placed a rush order for a particular raw material with two different suppliers, A and B. If neither order arrives in 4 days, the production process must be shut down until at least one of the orders arrives. The probability that supplier A can deliver the material in 4 days is 0.55 and the probability that supplier B can deliver the material in 4 days is 0.35. Assuming that the suppliers are independent of each other, what is the probability the production process is shut down in 4 days (both orders are late)?
(a) 0.1925
(b) 0.2000
(c) 0.2925
(d) 0.7075
(e) 0.8075

(50) A certain basketball player is fouled and awarded two free-throws. The probability that this player makes the first shot is 80%. If he makes the first shot, the probability that he makes the second shot increases to 90%. What is the probability that this player makes both free-throws?
(a) 0.64
(b) 0.72
(c) 0.85
(d) 0.89
(e) 0.98

(51) A medical researcher is investigating the pulse rates of smokers (population 1) and the pulse rates of nonsmokers (population 2). A sample of 100 smokers had a mean of 90 and a standard deviation of 5. A sample of 100 nonsmokers had a mean of 88 and a standard deviation of 6. What are the null and alternative hypotheses that would be used to determine if the variability of the pulse rates of the smokers is different than the variability of the pulse rates of the nonsmokers?
(a) H0: m1 - m2 ³ 0 vs. Ha: m1 - m2 < 0
(b) H0: s 12/s 22 £ 1 vs. Ha: s 12/s 22 > 1
(c) H0: m1 - m2 = 0 vs. Ha: m1 - m2 (not =) 0
(d) H0: s 12/s 22 ³ 1 vs. Ha: s 12/s 22 < 1
(e) H0: s 12/s 22 = 1 vs. Ha: s 12/s 22 (not =) 1

ANSWERS

(1) D (2) A (3) D (4) C (5) D (6) B (7) E (8) E (9) D (10) E
(11) D (12) E (13) B (14) A (15) A (16) B (17) D (18) C (19) C (20) D
(21) E (22) B (23) D (24) E (25) C (26) A (27) C (28) C (29) C (30) B
(31) A (32) E (33) B (34) B (35) B (36) B (37) B (38) E (39) B (40) D
(41) C (42) D (43) D (44) E (45) D (46) C (47) B (48) C (49) C (50) B (51) E

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