Download Test 3 Answer Key - Essential Mathematics | MTHSC 101 and more Exams Mathematics in PDF only on Docsity!
Multiple Choice Section: 16 Questions (3 points each) for a total of 48 points. Circle the correct
answer on the test (for your reference later) and then enter it in the appropriate location on the
Scantron form. Your answers on this portion of the test will be graded by Scantron only.
- In a stack of 57 tax returns, five returns have errors. If an IRS auditor selects three returns at random, what is the probability that she selects none of those that contain errors?
A. 0. B. 0. C. 0. D. 0.
- Suppose you must choose a three course meal. You have 3 options for your appetizer, 2 options for your main course, and 4 options for dessert. How many different meal choices do you have?
A. 48 B. 24 C. 12 D. 288
- You are playing a game in which each bet has an expected value of -$0.50. This means that:
A. if you play many times, on average you will lose $0.50 for each time you play. B. if you play many times, on average you will win $0.50 for each time you play. C. you will lose $0.50 every time you play. D. you will win $0.50 every time you play.
- In the second round of a tennis tournament there is the following situation: The probability that Anne will play is 1/6. The probability that Bette will play is 1/2. Whether either of these players will play depends somewhat on if the other is playing. The probability that Anne will play, given that Bette is playing, is 1/9. The probability that Bette will play, given that Anne is playing, is 1/3. Find the probability that Anne and Bette will both play.
A. 1/ B. 1/ C. 1/ D. 1/
- Suppose the weight of vehicles parked at Clemson is normally distributed with mean 2500 pounds and standard deviation 300 pounds. There are 7000 vehicles total. Approximately how many vehicles weigh between 2500 and 3100 pounds?
A. 4760 B. 6650 C. 2380 D. 3325
- Teams participating in a Bocce tournament must declare, prior to each match, which players will throw first, second, third and fourth. A Bocce club with ten members must select the four who will participate and declare the order in which they will compete. Given ten possible players and the four positions, how many lineups are possible?
A. 210 B. 5040 C. 252 D. 10000
- Alice is among 300 people to take a standardized test. She is told that she scored 0.15 standard deviations above the mean. Fill in the blank: Alice scored higher than approximately _______ people.
A. 168 B. 279 C. 21 D. 132
- A student council with eight members must appoint a 4-person committee to plan the Senior Prom. How many different committees are possible?
A. 1680 B. 101 C. 4096 D. 70
- What is the probability that you randomly meet someone whose phone number has the same last digit as your phone number?
A. 1/ B. 1/ C. 1/ D. 1/
- An insurance policy sells for $250. Based on past data, an average of 1 in 100 policy holders will file a $10,000 claim, and an average of 1 in 500 will file a $50,000 claim. Find the expected value to the company per policy sold.
A. -$ B. $ C. $ D. -$
- 167 men and women were asked a particular question. All of them answered either “Yes” or “No.” Of the 89 people who answered “Yes” to the question, 12 were male and 77 were female. Of the 78 people who answered “No” to the same question, 11 were male and 67 were female. If one person is randomly selected from the group, find the probability that this person answered “Yes” or is male.
A. 0. B. 0. C. 0. D. 0.
- Find the probability of drawing at least one club when you draw 11 cards from a standard deck. Assume that you replace the card each time you draw, so that there always are 52 cards from which to choose.
A. 0. B. 0. C. 0. D. 0.
End of multiple choice. Check to make sure you have bubbled in 16 answers for 16 questions.
Free Response Section: The following questions will be graded by hand. Show all necessary work and
make sure that your answers are responsive to the question and are legible and complete. Verify that the
answers carry the appropriate units. Illegible work will be considered wrong. You may show your answers to
problems dealing with probability either as fractions or decimals with FOUR places past the decimal.
- Suppose a university requires applicants to score at or above the 84th^ percentile on both the Mathematics and Critical Reading portions of the SAT to be considered for admittance.
27,600 students took this test. The scores for both portions are distributed approximately normally.
The Mathematics portion has mean 515 and standard deviation 116.
The Critical Reading portion has mean 502 and standard deviation 112.
a. Approximately how many people scored between 399 and 747 on the Mathematics portion?
27,600 x .815 = 22494 Must show appropriate work 2
Answer: 22,
b. What Critical Reading score was required for a student to be in the 84th^ percentile?
84 th^ percentile → Z = 1 = X – 502 So X = 614 112 Must show appropriate work 2
Answer: 614
c. If George scored 650 on the Mathematics, did he score high enough to be considered? Show all work necessary to justify your answer.
Z = 650 – 515 = 1. 116 Must show appropriate work 2 Choose one: NO, because George is only in the __________ percentile.
YES, because George is in the 86 th^ percentile.
- Suppose a $1 lottery ticket has the following probabilities for winning:
There is a 1 in 25 chance to win $ There is a 1 in 100 chance to win $ There is a 1 in 500 chance to win $ There is a 1 in 100,000 chance to win $
a. Compute the expected value of buying a lottery ticket.
X (winnings, $) P(X) X • P(X) 5 1/25. 50 1/100. 100 1/500. 1000 1/100,000. . 2
Expected value = E(winnings) – Cost = $0.91 - $1.00 = - $0.
Must show appropriate work
Answer: 2
b. If you buy 200 lottery tickets, how much should you expect to win/lose? Fill in the appropriate blank.
I expect to win $__________ I expect to lose $ 18.00 2
- You toss two fair, four-sided dice. Each die has a 2, 3, 4 or 5 appearing on the different four sides.
a. List of All Possible Outcomes
b. Complete the Probability Distribution, where x = the sum of the dice
x P(x) 4 1/16 or. 5 2/16 or. 6 3/16 or. 7 4/16 or. 8 3/16 or. 9 2/16 or. 10 1/16 or. 1
Must show all outcomes 4
Compute P(x < 8) = 1/16 + 2/16 + 3/16 + 4/16 = .625 or 5/
Answer: 2
8
- A college requires that all students establish a password for their computer account which is four characters long. This password is comprised of any of 26 letters, all lower case, and repetition is permitted. How many unique passwords are possible?
26 x 26 x 26 x 26 = 264 1
Answer: 2
This same university requires that faculty and administrators establish a stronger password. These users must have a five-character password. Four of the spaces are to be any of 26 letters, all lower case, and repetition is not permitted. The remaining space is to be occupied by either a strong character ($, # or @), or a number (0-9). How many unique passwords are possible?
26 x 25 x 24 x 23 x 13
Or: 26 P 4 x 13 1
Answer: 2
- You are playing a card game where every player is dealt 3 cards from a standard 52-card deck.
a. How many possible hands are there? 52 C 3 2
Answer: 1
b. What is the probability of being dealt three cards and getting, among the four cards, exactly 2 Jacks?
4 C 2 x^48 C 1 6 x^48 52 C 4 22,
Answer: 1
c). What is the probability of being dealt three cards which are in the same suit?
This is the probability that they all come from the same suit…
13 C 3 x^39 C 0 =^286 x^1 =^. 52 C 3 22,100^ But there are 4 suits, so .0129 x 4 =.
Or: 52 x 12 x 11 = .0518 2 52 51 50
Answer: 1
