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

Unit Test — Unit test Answers

15 verified answers
1
Free Preview

Hannah and Claire each have a chicken coop with 6 hens. Let H represent the total number of eggs the hens lay on a randomly chosen day in Hannah’s coop and let C represent the total number of eggs the hens lay on a randomly chosen day in Claire’s coop. The two distributions are displayed in the table and histograms.

Question illustration
A
The standard deviation for Hannah’s eggs is 1.4, and the standard deviation for Claire’s eggs is 1.6.
B
The standard deviation of the number of eggs laid by Claire’s hens is greater than the standard deviation of the number of eggs laid by Hannah’s hens.
C
The standard deviation of the number of eggs laid by Claire’s hens is less than the standard deviation of the number of eggs laid by Hannah’s hens.
D
The standard deviation of the number of eggs laid by Hannah’s hens is about the same as the standard deviation of the number of eggs laid by Hannah’s hens
2
Free Preview

A bottled water company runs a promotion in which 1 out of every 4 bottles has the word "Winner” printed under the cap. Winners receive a free bottle of water. A store owner notices that in the last 4 bottles of water purchased, 2 have been winners. Using the table, what is the probability of getting 2 or more "Winner” caps on 4 bottles of water?

Question illustration
A
0.211
B
0.262
C
0.738
D
0.949
3

A shipping company claims that 95% of packages are delivered on time. A student wants to conduct a simulation to estimate the number of packages that would need to be randomly selected in order to find a package that was not delivered on time. The student assigns the digits to the outcomes. 00-04 = package not delivered on time05-99 = package delivered on time

A
Read 100 two-digit numbers. Count the number of packages that were not delivered on time.
B
Read two-digit numbers. Count the number of packages that are needed in order to find one that was delivered on time.
C
Read two-digit numbers. Count the number of packages that are needed in order to find one that was not delivered on time.
D
Read 100 two-digit numbers. Count the number of packages that are needed in order to find one that was not delivered on time.
4

Sisters Amilia and Bianca play games together often. Let A represent the number of games Amilia wins monthly, and let B represent the number of games Bianca wins monthly. A and B are independent events. The mean of A is 35.7 games with a standard deviation of 5.1 games, and the mean of B is 37.3 games with a standard deviation of 6.8 games. What is the mean and standard deviation of the total number of games won, S = A + B?

A
= 54.4 games and = 3.4 games.
Option A
B
= 54.4 games and = 11.9 games.
Option B
C
= 73.0 games and = 8.5 games.
Option C
D
= 73.0 games and = 11.9 games.
Option D
5

Based on their own blood types, a couple has a 0.75 probability of having a child with type A blood. If the couple has 4 children, what is the probability that they will have 2 children with type A blood?

A
0.07
B
0.21
C
0.56
D
0.75
6

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. What is an appropriate assignment of digits for this simulation?

A
Let 01-08 = the carton contains a broken egg. Let 09-99 and 00 = the carton does not contain a broken egg.
B
Let 09-99 and 00 = the carton contains a broken egg. Let 01-08 = the carton does not contain a broken egg.
C
Let 1-8 = the carton contains a broken egg. Let 9 and 0 = the carton does not contain a broken egg.
D
Let 9 and 0 = the carton contains a broken egg. Let 1-8 = the carton does not contain a broken egg.
7

Two different furniture manufacturers produce chairs. Let X represent the number of chairs produced daily at plant X, and let Y represent the number of chairs produced daily at plant Y. Assume that X and Y are independent random variables. Which of the following choices explains the meaning of independent random variables in context?

A
The independence of the two manufacturers means that the two random variables have a correlation of 1.
B
The independence of the two manufacturers means that the number of chairs produced is approximately Normal.
C
The independence of the two manufacturers means that knowing how much one furniture plant produces does not help us predict how much the other produces.
D
The independence of the two manufacturers means that if one plant is producing chairs properly, the other has a smaller probability of producing chairs properly.
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.Which is the correct interpretation of the standard deviation?

Question illustration
A
If many, many free throws are attempted, the expected number made would be 4.8 free throws.
B
The number of free throws made out of 8 typically varies from the expected value by 1.4 free throws.
C
The mean number of free throws made typically varies from the expected number of free throws made by 1.4 free throws.
D
The number of free throws made out of 8 typically varies from the expected number of free throws made by 1.96 free throws.
9

In a certain board game, a 12-sided number cube showing numbers 1–12 is rolled. In this game, a number cube must be rolled until a number 9 or higher appears.

A
Yes, the geometric distribution is appropriate.
B
No, since each trial is not independent of the other trials.
C
No, because it is not looking for the first occurrence of success.
D
No, since a success and failure on each trial cannot be defined.
10

A volleyball player’s serving percentage is 90%. Six random serves are selected. What is the probability that 5 of those serves were successful?

A
0.09
B
0.35
C
0.59
D
0.90
11

Claire flips a coin 4 times. Using the table, what is the probability that the coin will show tails at most once?

Question illustration
A
0.06
B
0.25
C
0.31
D
0.69
12

A shipping company claims that 95% of packages are delivered on time. A student wants to conduct a simulation to estimate the number of packages that would need to be randomly selected in order to find a package that was not delivered on time. What is an appropriate assignment of digits to carry out this simulation?

A
Let 00-04 = not delivered on time. Let 05-99 = delivered on time.
B
Let 05-99 = not delivered on time. Let 00-04 = delivered on time.
C
Let 00-05 = not delivered on time. Let 06-99 = delivered on time.
D
Let 06-99 = not delivered on time. Let 00-05 = delivered on time.
13

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 given in the table.

Question illustration
A
A histogram titled number of eggs has x = number of eggs on the x-axis, and probability on the y-axis. 0, 0.18; 1, 0.28; 2, 0.30; 3, 0.12; 4, 0.07; 5, 0.03; 6. 0.02.
Option A
B
A histogram titled number of eggs has x = number of eggs on the x-axis, and probability on the y-axis. 0, 0.02; 1, 0.03; 2, 0.17; 3, 0.30; 4, 0.20; 5, 0.18; 6, 0.10.
Option B
C
A histogram titled number of eggs has x = number of eggs on the x-axis, and probability on the y-axis. 0, 0.13; 1, 0.12; 2, 0.13; 3, 0.12; 4, 0.13; 5, 0.12; 6, 0.12.
Option C
D
A histogram titled number of eggs has x = number of eggs on the x-axis, and probability on the y-axis. 0, 0.02; 1, 0.03; 2, 0.07; 3, 0.12; 4, 0.30; 5, 0.27; 6, 0.18.
Option D
14

A produce company packages presliced celery and carrots. Let X represent the length of a slice of celery, and let Y represent the length of a slice of carrot. X and Y are independent events. The mean of X is 2.5 inches with a standard deviation of 0.6 inches, and the mean of Y is 2.25 inches with a standard deviation of 0.4 inches. What is the mean and standard deviation of the difference, D = X – Y?

A
= –0.25 inches and = 0.2 inches
Option A
B
= –0.25 inches and = 0.45 inches
Option B
C
= 0.25 inches and = 0.52 inches
Option C
D
= 0.25 inches and = 0.72 inches
Option D
15

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 given in the table.Which of the following represents the probability of the hens laying at least four eggs?

Question illustration
A
P(X > 4)
B
P(X ≥ 4)
C
P(X < 4)
D
P(X ≤ 4)

Did you find these answers helpful?

More from this Course

Quiz
15 verified answers

Unit Test

Quiz
15 verified answers

Unit Test

Quiz
15 verified answers

Unit Test

Unit Test — Unit test Answers — Probability and…