Mathematics
. In a poll, respondents were asked whether they had ever been in a car accident. 220 respondents indicated that they had been in a car accident and 370 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? Round to the nearest thousandth.A. 0.384 B. 0.380 C. 0.373D. 0.370
P(accident) = 220 / (220 + 370) = 0.373
2. 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 one head?
A. 4/9 B. 5/6 C. 7/8 D. 5/8
P(at least one head) = (Number of combinations with one or more H) / (Total number of combinations)
P(at least one head) = 7 / 8
3. Joe dealt 20 cards from a standard 52card 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.
1^{st} deal: 14 red and 6 black P(red) = 14/20 = 0.70
2^{nd} deal: 20 red and 10 black P(red) = 20/30 = 0.67 < 0.70
4. Suppose you have an extremely unfair die: The probability of a 6 is 3/8, and the probability of each other number is 1/8. If you toss the die 32 times, how many twos do you expect to see?A. 2 B. 4 C. 3 D. 5
E(2) = np = 32(1/8) = 4
5. 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. 25/66C. 50/132 D. 82/132
P(woman) = 50 / (50 + 82) = 50/132 = 25/66
6. 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
P(two consecutive H) = (Number of combinations with HH) / (Total number of combinations)
P(two consecutive H) = 3/8
7. 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
E(x) = (1/1000)($500) – 1 = $0.50 – $1 = $0.50
8. 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
P(at least 2 T) = (Number of combinations with 2 or more T) / (Total number
of combinations)
P(at least 2 T) = 4/8 = ½
9. A bag contains four chips of which one is red, one is blue, one is green, and one is yellow. A chip is selected at random from the bag and then replaced in the bag. A second chip is then selected at random. Make a list of the possible outcomes (for example, RB represents the outcome red chip followed by blue chip) and use your list to determine the probability that the two chips selected are the same color. (Hint: There are 16 possible outcomes.)A. 1/4 B. ¾ C. 2/16 D. 3/16
Possible outcomes: RR RB RG RY
BR BB BG BY
GR GB GG GY
YR YB YG YY
P(two of same color) = (Number of combinations with same color) / (Total
number of combinations)
P(two of same color) = 4/16 = ¼
10. 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
Sample space: ABC ABD ABE ACD ACE
ADE BCD BCE BDE CDE
P(combination includes B) = (Number of combinations including B) / (Total
number of combinations)
P(combination includes B) = 6/10 = 0.6
11. 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.
12. 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.
Monday: 9 odd, 3 even P(odd) = 9/12 = 0.75
Tuesday: 13 odd, 5 even P(odd) = 13/18 ≈ 0.722 < 0.75
13. 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
E(x) = (1/3)($3) – $1 = $1 – $1 = $0
14. On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?
A. 1/5 B. 1/6 C. 1/4 D. 2/5
P(correct) = Number of correct answers / Number of possible choices
P(correct) = 1/6
15. 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.
16. 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
P(not in Business) = (Number not in Business) / Total number of degrees
P(not in Business) = (9313 – 1676) / 9313
P(not in Business) = 0.8200
17. A 28yearold man pays $125 for a oneyear 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
E(x) = (1 – 0.9994)($140,000) – $125 = $41
18. 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
P(blue) = Number of blue marbles / Total number of marbles
P(blue) = 3 / (4 + 3 + 7) = 3/14
19. 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
P(salary ≥ $98,000) = Number of salaries ≥ 98,000 / Total number of salaries
P(salary ≥ $98,000) = 14/20 = 0.7
20. A study of students taking Statistics 101 was done. Four hundred students who studied for more than 10 hours averaged a B. Two hundred students who studied for less than 10 hours averaged a C. This difference was significant at the 0.01 level. What does this mean?
A. The probability that the difference was due to chance alone is greater than 0.01.
B. There is less than a 0.01 chance that the first group’s grades were better by chance alone.
C. The improvement was due to the fact that more people studied.
D. There is not enough information to make any conclusion
21. Sample size = 400, sample mean = 44, sample standard deviation = 16. What is the margin of error?
A. 1.4 B. 1.6 C. 2.2 D. 2.6
Assuming a 95% confidence level, and noting that this class seems to use z = 2 for this confidence level instead of the more accurate 1.96 value.
E = z*s/√n = 2 * 16 / √400 = 1.6
22. 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
23. 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
Again, assuming a 95% confidence interval, with z = 2.00 instead of 1.96:
n = (z * s / E)^{2} = (2 * 248 / 30)^{2} = 273.35 à 274
24. 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.
