AnswersNC-Math 4Binomial Probabilities

Binomial Probabilities — Unit test Answers

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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
2
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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)
3

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
4

A small university has 200 first-year students. Historically at this university, 88% of first-year students graduate in four years. Assume that whether or not one student graduates is independent of whether or not another student graduates. Let X represent the number of first-year students who graduate in four years. What are the mean and standard deviation X?

A
Mu Subscript x Baseline = 100, Sigma Subscript x Baseline = 0.88
Option A
B
Mu Subscript x Baseline = 176, Sigma Subscript x Baseline = 21.12
Option B
C
Mu Subscript x Baseline = 176, Sigma Subscript x Baseline = 4.60
Option C
D
Mu Subscript x Baseline = 188, Sigma Subscript x Baseline = 24
Option D
5

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
6

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let X represent the score on a randomly selected exam. The distribution of scores for one subject’s standardized test is given in the table.

Question illustration
A
1.3
B
1.6
C
1.7
D
2.5
7

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.
8

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
9

Consider the given probability histogram of a binomial random variable.

Question illustration
A
Center: 2Shape: skewed left
B
Center: 2.4Shape: skewed right
C
Center: 2.4Shape: skewed left
D
Center: 3.Shape: skewed right
10

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
11

Ten membersThree juniors and seven seniors from the science club qualify for a national competition, but only five people per school can attend the event. The coach decides to put the 10 members’ names on identical slips of paper, put the slips in a hat, and pull out five names, one at a time. Those five students will go to the national competition. Let X represent the number of juniors selected to attend the competition.Have the conditions for a binomial setting been met for this scenario?

A
Yes, all four conditions in BINS have been met.
B
No, we do not know how many people overall will go to the national competition.
C
No, there is no way to find out the probability of choosing just one student to attend.
D
No, the names were pulled and not replaced in the hat, so the independence condition is not met.
12

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 expected value of the distribution?

Question illustration
A
4
B
4.5
C
4.8
D
5
13

A racecar driver has a 0.05 probability of winning any given race in a season. There are 16 races in a season, and whether or not the driver wins one race is independent of whether he wins any other race. Let X represent the number of races the driver wins in the season.Have the conditions for a binomial setting been met for this scenario?

A
No, a sample size of 16 races is too small.
B
Yes, all four conditions in BINS have been met.
C
No, the probability of winning is too small for a binomial setting.
D
Yes, but they will only have been met if the racecar driver improves the probability of winning a race as the season progresses.
14

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.What is the probability that the hens lay more than two eggs?

Question illustration
A
0.07
B
0.12
C
0.88
D
0.95
15

One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The histogram displays the distribution.

Question illustration
A
slightly skewed left
B
slightly skewed right
C
unimodal, symmetric
D
strongly skewed left

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