AnswersProbability and Statistics with Applications Honors Sem-2-FL-1210300 2024-2025Unit Test

Unit Test — Unit test Answers

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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
2
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Renee and Thomas live at the beach and collect seashells. The number of shells Renee collects on any given day, R, is approximately Normal with a mean of 58.2 shells and a standard deviation of 12.8 shells. The number of shells Thomas collects on any given day, T, is approximately Normal with a mean of 47.9 shells and a standard deviation of 11.5 shells. Assume the two random variables are independent of each other.What is the probability that on a randomly selected day the total number of shells collected by Renee and Thomas is 120 or more?

A
0.002
B
0.209
C
0.284
D
0.791
3

Based upon historical data, it is known that 8% of 12-egg cartons contain at least one broken egg. A grocery store manager would like to carry out a simulation to estimate the number of cartons, in a sample of 10, that would contain at least one broken egg. She assigns the digits to the outcomes:01-08 = carton contains a broken egg09-99, 00 = carton does not contain a broken eggHere is a portion of a random number table.In the first trial, line 1, one of the first 10 double-digit numbers is between 01 and 08, meaning that 1 of the 10 cartons of eggs contains at least one broken egg. Starting at line 2 and using a new line for each trial, carry out 4 more trials. In what proportion of these 5 trials is there no carton with broken eggs?

Question illustration
A
0
B
0.2
C
0.4
D
0.6
4

A medical device company knows that the percentage of patients experiencing injection-site reactions with the current needle is 11%. What is the standard deviation of X, the number of patients seen until an injection-site reaction occurs?

A
3.1289
B
8.5763
C
9.0909
D
11
5

Based upon historical data, it is known that 8% of 12-egg cartons contain at least one broken egg. A grocery store manager would like to carry out a simulation to estimate the number of cartons, in a sample of 10, that would contain at least one broken egg. She assigns the digits to the outcomes:01-08 = carton contains a broken egg09-99, 00 = carton does not contain a broken eggHere is a portion of a random number table.Beginning at line 1, carry out one trial of this simulation. Use additional lines as needed. How many cartons in this random sample of 10 cartons contain at least one broken egg?

Question illustration
A
0
B
1
C
2
D
3
6

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.
7

A commuter train is late to a station 5% of the time. Last week, the train was late on 2 of the 7 days. If the train being late can be considered a random event, what is the probability that the train would be late 2 times in 7 days?

A
0.004
B
0.014
C
0.041
D
0.050
8

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
9

There are 16 students in a science class. Let X represent the number of students born on a Tuesday. Assuming birthdays in this class are independent of one another, what are the mean and standard deviation of X?

A
Mu Subscript x Baseline = 2.29, Sigma Subscript x Baseline = 1.40
Option A
B
Mu Subscript x Baseline = 3, Sigma Subscript x Baseline = 1.96
Option B
C
Mu Subscript x Baseline = 7, Sigma Subscript x Baseline = 1.51
Option C
D
Mu Subscript x Baseline = 13.71, Sigma Subscript x Baseline = 3.84
Option D
10

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.
11

A jar contains 11 red marbles, 12 blue marbles, and 6 white marbles. Four marbles from this jar are selected, with each marble being replaced after each selection. What is the probability that the first red marble chosen is on the 5th selection?

A
0.0128
B
0.0563
C
0.1484
D
0.2815
12

A fair, six-sided number cube has the numbers 2, 2, 4, 4, 6, 6 on its faces. Sarah rolls this number cube 10 times and records the number of times a 2 is rolled.Have the conditions for a binomial setting been met for this scenario?

A
Yes, all four conditions in BINS have been met.
B
No, the rolls of a number cube are not independent of one another.
C
No, this is not a fair number cube because each outcome shows on more than one face.
D
No, without any odd-numbered faces, we cannot determine the probability of rolling a 2.
13

At a carnival game, the chance of winning a prize is 0.45. Kylee plays the game 3 times. Using the table, what is the probability that she wins at most 2 prizes?

Question illustration
A
0.09
B
0.33
C
0.58
D
0.91
14

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
15

Let A represent the battery life of a brand A laptop, and let B represent the battery life of a brand B laptop. The mean difference in battery life between these two brands of laptops, D = A – B, is –3.25 hours. What is the correct interpretation of this value?

A
On average, brand B gains 3.25 hours of battery life daily.
B
On average, brand A loses 3.25 hours of battery life daily.
C
Both brands are typically losing 3.25 hours of battery life daily.
D
On average, brand B’s battery life lasts 3.25 hours longer than brand A.
16

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
17

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
18

At a carnival game, the chance of winning a prize is 0.45. Elijah plays the game 5 times. What is the probability that he wins 1 prize in 5 games?

A
0.04
B
0.05
C
0.21
D
0.45
19

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.
20

A placekicker for a football team makes field goals 55% of the time when kicking from the 35-yard line. Assume that field goal attempts can be considered random events. Using the table, what is the probability that the placekicker will make at least 3 of his next 5 attempts from the 35-yard line?

Question illustration
A
0.34
B
0.26
C
0.60
D
0.74

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