Question 1:
Of 1308 people who came into a blood bank to give blood, 314 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure (to 3 decimal places).
A. 0.250
B. 0.490
C. 0.240
D. 0.160
Question 2:
Suppose you have an extremely unfair coin: the probability of a head is 1/5, and the probability of a tail is 4/5. If you toss the coin 40 times, how many heads do you expect to see?
A. 8
B. 6
C. 5
D. 4
Question 3
A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?
A. 2/11
B. 3/11
C. 5/14
D. 3/14
Question 4
The probability that Luis will pass his statistics test is 0.94. Find the probability that he will fail his statistics test.
A. 0.02
B. 0.05
C. 0.94
D. 0.06
Question 5
A sample space consists of 46 separate events that are equally likely. What is the probability of each?
A. 1/24
B. 1/46
C. 1/32
D. 1/18
Question 6
The distribution of B.A. degrees conferred by a local college is listed below, by major.
Major Frequency
English 2073
Mathematics 2164
Chemistry 318
Physics 856
Liberal Arts 1358
Business 1676
Engineering 868
9313
What is the probability that a randomly selected degree is not in Business?
A. 0.7800
B. 0.8200
C. 0.8300
D. 0.9200
Question 7
A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.)
A. 0.6
B. 0.4
C. 0.7
D. 0.8
Question 8
A 28-year-old man pays $125 for a one-year life insurance policy with coverage of $140,000. If the probability that he will live through the year is 0.9994, to the nearest dollar, what is the man's expected value for the insurance policy?
A. $139,916
B. -$41
C. $84
D. -$124
Question 9
Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio of odd/even expected of such a series of temperature checks.
A. The Monday series is closer because 1/6 is closer to 1/2 than is 1/8.
B. The Monday series is closer because 6/12 is closer to 0.5 than is 8/18.
C. The Tuesday series is closer because the 13/18 is closer to 0.5 than is 9/12.
D. The series closest to the theoretical 50/50 cannot be determined without knowing the number of odds and evens in each series
Question 10
If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that at least two heads occur consecutively?
A. 1/8
B. 3/8
C. 5/8
D. 6/8
Question 11
A class consists of 50 women and 82 men. If a student is randomly selected, what is the probability that the student is a woman?
A. 32/132
B. 25/66
C. 50/132
D. 82/132
Question 12
The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $98,000.
112,000 126,000 90,000 133,000 94,000 112,000 98,000 82,000 147,000 182,000 86,000 105,000
140,000 94,000 126,000 119,000 98,000 154,000 78,000 119,000
A. 0.4
B. 0.6
C. 0.66
D. 0.7
Question 13
Suppose you have an extremely unfair coin: the probability of a head is 1/3 and the probability of a tail is 2/3. If you toss the coin 72 times, how many heads do you expect to see?
A. 12
B. 22
C. 24
D. 26
Question 14
In the first series of rolls of a die, the number of odd numbers exceeded the number of even numbers by 5. In the second series of rolls of the same die, the number of odd numbers exceeded the number of even numbers by 11. Determine which series is closer to the 50/50 ratio of odd/even expected of a fairly rolled die.
A. The second series is closer because the difference between odd and even numbers is greater than the difference for the first series.
B. The first series is closer because the difference between odd and even numbers is less than the difference for the second series.
C. Since 1/2 > 1/5 > 1/11, the first series is closer.
D. The series closer to the theoretical 50/50 cannot be determined unless the total number of rolls for both series is given.
Question 15
If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least two tails?
A. 1/2
B. 2/3
C. 3/4
D. 4/9
Question 16
Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.413. Find the probability that in a given year it will not snow on January 1st in that town.
A. 0.345
B. 0.425
C. 0.587
D. 0.592
Question 17
A study of two types of weed killers was done on two identical weed plots. One weed killer killed 15% more weeds than the other. This difference was significant at the 0.05 level. What does this mean?
A. The improvement was due to the fact that there were more weeds in one study.
B. The probability that the difference was due to chance alone is greater than 0.05.
C. The probability that one weed killer performed better by chance alone is less than 0.05.
D. There is not enough information to make any conclusion.
Question 18
Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $500. What is your expected value?
A. $0.00
B. -$0.40
C. -$1.00
D. -$0.50
Question 19
Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 5 or a 2, nothing otherwise. What is your expected value?
A. $1.00
B. $0.00
C. $3.00
D. -$1.00
Question 20
Joe dealt 20 cards from a standard 52-card deck, and the number of red cards exceeded the number of black cards by 8. He reshuffled the cards and dealt 30 cards. This time, the number of red cards exceeded the number of black cards by 10. Determine which deal is closer to the 50/50 ratio of red/black expected of fairly dealt hands from a fair deck and why.
A. The first series is closer because 1/10 is farther from 1/2 than is 1/8.
B. The series closer to the theoretical 50/50 cannot be determined unless the number of red and black cards for each deal is given.
C. The second series is closer because 20/30 is closer to 1/2 than is 14/20.
D. The first series is closer because the difference between red and black is smaller than the difference in the second series.
Question 21
The graph shows a measure of fitness (y) and miles walked weekly. Identify the probable cause of the correlation.
A. The correlation is coincidental.
B. There is a common underlying cause of the correlation.
C. There is no correlation between the variables.
D. Walking is a direct cause of the fitness
Question 22
A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 490 college students showed that 33% of them had, or intended to, cheat on examinations. Find the margin of error for the 95% confidence interval.
A. 0.0432
B. 0.0434
C. 0.0425
D. 0.0427
Question 23
30% of the fifth grade students in a large school district read below grade level. The distribution of sample proportions of samples of 100 students from this population is normal with a mean of 0.30 and a standard deviation of 0.045. Suppose that you select a sample of 100 fifth grade students from this district and find that the proportion that reads below grade level in the sample is 0.36. What is the probability that a second sample would be selected with a proportion less than 0.36?
A. 0.8932
B. 0.8920
C. 0.9032
D. 0.9048
Question 24
Select the best fit line on the scatter diagram below.
A. A
B. B
C. C
D. None of the lines is the line of best fit
Question 25
A sample of nine students is selected from among the students taking a particular exam. The nine students were asked how much time they had spent studying for the exam and the responses (in hours) were as follows:
18, 7, 10, 13, 12, 16, 5, 20, 21
Estimate the mean study time of all students taking the exam. Round your answer to the nearest tenth of an hour if necessary.
A. 13 hours
B. 12.2 hours
C. 13.6 hours
D. It is not possible to estimate the population mean from this sample data
Question 26
Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.
A. 0.60
B. -0.97
C. 0.10
D. -0.60
Question 27
Which point below would be an outlier if it were on the following graph?
A. (25, 20)
B. (5, 12)
C. (7, 5)
D. (5, 3)
Question 28
Suggest the cause of the correlation among the data.
The graph shows strength of coffee (y) and number of scoops used to make 10 cups of coffee (x). Identify the probable cause of the correlation.
A. The variation in the x variable is a direct cause of the variation in the y variable.
B. There is no correlation between the variables.
C. The correlation is due to a common underlying cause.
D. The correlation between the variables is coincidental.
Question 29
Of the 6796 students in one school district, 1537 cannot read up to grade level. Among a sample of 812 of the students from this school district, 211 cannot read up to grade level. Find the sample proportion of students who cannot read up to grade level.
A. 0.14
B. 0.26
C. 211
D. 0.23
Question 30
A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a margin of error E = 0.01with a 95% degree of confidence.
A. 7,000
B. 8,000
C. 9,000
D. 10,000
Question 31
A researcher wishes to estimate the mean amount of money spent per month on food by households in a certain neighborhood. She desires a margin of error of $30. Past studies suggest that a population standard deviation of $248 is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.
A. 274
B. 284
C. 264
D. 272
Question 32
Which graph has two groups of data, correlations within each group, but no correlation among all the data?
Question 33
Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.
A. -0.9
B. 0.1
C. 0.5
D. 0.9
Question 34
Monthly incomes of employees at a particular company have a mean of $5954. The distribution of sample means for samples of size 70 is normal with a mean of $5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that their mean monthly income is $5747. How many standard deviations is the sample mean from the mean of the sampling distribution?
A. 0.8 standard deviations above the mean
B. 0.8 standard deviations below the mean
C. 7.3 standard deviations below the mean
D. 207 standard deviations below the mean
Question 35
Select the best fit line on the scatter diagram below.
A. A
B. B
C. C
D. All of the lines are equally good
Question 36
The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Determine the amount of variation in the number of cars not explained by the variation time after school.
A. 55%
B. 70%
C. 30%
D. 45%
Question 37
The scatter plot and best-fit line show the relation between the price per item (y) and the availability of that item (x) in arbitrary units. The correlation coefficient is -0.95. Determine the amount of variation in pricing explained by the variation in availability.
A. 5%
B. 10%
C. 95%
D. 90%
Question 38
Among a random sample of 150 employees of a particular company, the mean commute distance is 29.6 miles. This mean lies 1.2 standard deviations above the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute distance will be less than 29.6 miles?
A. 0.8849
B. 0.5
C. 0.1131
D. 0.1151
Question 39
The scatter plot and best-fit line show the relation among the data for the price of a stock (y) and employment (x) in arbitrary units. The correlation coefficient is 0.8. Predict the stock price for an employment value of 6.
A. 8.8
B. 6.2
C. 8.2
D. None of the values are correct
Question 40
A sample of 64 statistics students at a small college had a mean mathematics ACT score of 28 with a standard deviation of 4. Estimate the mean mathematics ACT score for all statistics students at this college. Give the 95% confidence interval.
A. 28.0 to 30.0
B. 25.0 to 27.0
C. 29.0 to 31.0
D. 27.0 to 29.0