AnswersEHS Content Recovery - Probability and Statistics - Part CUnit Test

Unit Test — Unit test Answers

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1
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Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let A represent the score on a randomly selected exam for subject A and let B represent the score on a randomly selected exam for subject B. The distributions of scores for each subject’s standardized tests are displayed in the table and the histograms.

Question illustration
A
Both distributions are roughly unimodal symmetric.
B
Subject A’s distribution is skewed right and subject B’s distribution is skewed left.
C
Subject A’s distribution is roughly unimodal symmetric and subject B’s distribution is skewed left.
D
Subject A’s distribution is roughly unimodal symmetric and subject B’s distribution is skewed right.
2
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The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table.

Question illustration
A
A histogram titled Movie tickets has x = number of tickets sold on the x-axis, and probability on the y-axis. 1, 0.55; 2, 0.20; 3, 0.17; 4, 0.06; 5, 0.02.
Option A
B
A histogram titled Movie tickets has x = number of tickets sold on the x-axis, and probability on the y-axis. 1, 0.02; 2, 0.17; 3, 0.20; 4, 0.55; 5, 0.06.
Option B
C
A histogram titled Movie tickets has x = number of tickets sold on the x-axis, and probability on the y-axis. 1, 0.17; 2, 0.55; 3, 0.20; 4, 0.06; 5, 0.02.
Option C
D
A histogram titled Movie tickets has x = number of tickets sold on the x-axis, and probability on the y-axis. 1, 0.02; 2, 0.17; 3, 0.55; 4, 0.20; 5, 0.06.
Option D
3

Two students have devised a dice game named “Sums” for their statistics class. The game consists of choosing to play odds or evens. Probabilities for “Sums”Roll23456789101112P(roll)Each person takes turns rolling two dice. If the sum is odd, the person playing odds gets points equal to the sum of the roll. If the sum is even, the person playing evens gets points equal to the sum of the roll. Note that the points earned is independent of who is rolling the dice.If Jessica is challenged to a game of Sums, which statement below is accurate in every aspect in guiding her to the correct choice of choosing to play odds or evens?

Question illustration
A
E(evens) will be more because there are more even numbers that result from rolling two dice. Therefore, Jessica should play evens.
B
E(odds) will be more because the probability for each odd number being rolled is greater. Therefore, Jessica should play odds.
C
E(evens) will be more because the value of the even numbers on the dice are more. Therefore, Jessica should play evens.
D
E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
4

You pick a card at random from an ordinary deck of 52 cards. If the card is a diamond, you get some points; if not, you lose 2 points. What value for the diamonds would make the game fair?

A
12
B
6
C
24
D
3
5

The owner of a local movie theater keeps track of the number of tickets sold in each purchase and makes a probability distribution based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table.

Question illustration
A
2
B
2.1
C
2.5
D
3
6

One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The distribution for X is shown in the table.What is the probability that the basketball player will make at least six free throws out of the eight attempts?

Question illustration
A
0.11
B
0.21
C
0.30
D
0.32
7

You are challenged to a lucky draw game. If you draw a face card (K, Q, J) from a standard deck of cards, you earn 10 points. If you draw any other card, you lose 2 points. What is the expected value of a draw?

A
0.77
B
1.69
C
1.85
D
2.31
8

A professional basketball player typically attempts 8 free throws per game. Let X represent the number of free throws made out of 8. The distribution for X is shown in the table.What is the median of the distribution?

Question illustration
A
4
B
4.5
C
4.8
D
5
9

The owner of a local movie theater keeps track of the number of tickets sold in each purchase and makes a probability distribution based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table.

Question illustration
A
The number of tickets purchased typically varies from the expected value by 0.95 tickets.
B
If many, many purchases are made, the expected number of tickets purchased is 2.1.
C
The mean number of tickets purchased typically varies from the expected value by 0.95 tickets.
D
The mean number of tickets purchased typically varies from the expected value by 0.89 tickets.
10

A local charity holds a carnival to raise money. In one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces with the values, 0, 1, 2, 5, and 10. Whatever space it lands on, the participant wins that value. Let X represent the value of a random spin. The distribution is given in the table.

Question illustration
A
The probability of a random spin having a value of at most 5 is 0.8.
B
The probability of a random spin having a value of at least 5 is 0.2.
C
The probability of a random spin having a value lower than 5 is 0.8.
D
The probability of a random spin having a value higher than 5 is 0.1.
11

Hannah has a chicken coop with six hens. Let X represent the total number of eggs the hens lay on a random day. The distribution for X is displayed in the histogram.

Question illustration
A
skewed left
B
skewed right
C
uniform, symmetric
D
approximately Normal
12

Black Marble Points

S
Since E(black) = 0.24 and E(red) = 0.16, Seth should choose to play black marbles.
E
E(red) will be twice that of E(black), so Seth should choose to play red marbles.
S
Since E(red) = E(black), it is a fair game, so it doesn’t matter which color Seth chooses.
B
Both options will lose points because there are two ways to lose points and only one way to gain points. He should choose neither color.
13

Joe takes part in math competitions. A particular contest consists of 25 multiple-choice questions, and each question has 5 possible answers. It awards 6 points for each correct answer, 1.5 points for each answer left blank, and 0 points for incorrect answers. Joe is sure of 12 of his answers. He ruled out 2 choices before guessing on 4 of the other questions and randomly guessed on the 9 remaining problems. What is his expected score?

A
69.2
B
75.6
C
90.8
D
97.2
14

The grade distribution for students in the introductory statistics class at a local community college are displayed in the table. In this table, A = 4, B = 3, etc. Let X represent the grade for a randomly selected student.

Question illustration
A
0.17
B
0.26
C
0.48
D
0.91
15

If a raffle has a winning prize of $100 and each ticket costs $5 with a total of 500 tickets sold, which equation would calculate the expected value?

A
100 (StartFraction 1 Over 500 EndFraction) + (negative 5) (StartFraction 499 Over 500 EndFraction) = E (X)
Option A
B
95 (StartFraction 1 Over 500 EndFraction) + (negative 5) (StartFraction 499 Over 500 EndFraction) = E (X)
Option B
C
(100 minus 5) (StartFraction 1 Over 500 EndFraction) = E (X)
Option C
D
(100) (StartFraction 1 Over 500 EndFraction) = E (X)
Option D
16

A company makes a $5 profit on each non-faulty product it sells. Approximately 2% of the products manufactured are faulty, with no way to discover which ones are faulty before delivery. If replacement-and-repair costs for the faulty products are $100 each, what is the profit per item?

A
loss of $15.10
B
loss of $15
C
profit of $2.90
D
profit of $3.00
17

The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is displayed in the histogram.

Question illustration
A
skewed left
B
skewed right
C
uniform, symmetric
D
approximately Normal
18

The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class.

Question illustration
A
2
B
3
C
2.98
D
3.50
19

The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class.

Question illustration
A
2
B
3
C
2.98
D
3.50
20

Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.Which is the correct interpretation of the standard deviation?

Question illustration
A
The number of eggs laid on a randomly selected day would typically vary from the expected number of eggs by 1.96 eggs.
B
The mean number of eggs laid on a randomly selected day would typically vary by 1.96 from the expected number of eggs.
C
The number of eggs laid on a randomly selected day would typically vary from the expected number of eggs by 1.4 eggs.
D
The mean number of eggs laid on a randomly selected day would typically vary by 1.4 from the expected number of eggs.

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