AnswersCollege Prep Math B - IC26Binomial Random Variables

Binomial Random Variables Answers

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The probability of a high school basketball team winning any game is 58%. This team is in a six-game tournament, and the games are played independently of one another. Let X represent the number of games the team might win in this tournament. What are the mean and standard deviation of X?

A
Mu Subscript x Baseline = 2.52, Sigma Subscript x Baseline = 2.15
Option A
B
Mu Subscript x Baseline = 3.48, Sigma Subscript x Baseline = 1.21
Option B
C
Mu Subscript x Baseline = 3.48, Sigma Subscript x Baseline = 1.46
Option C
D
Mu Subscript x Baseline = 5, Sigma Subscript x Baseline = 1.46
Option D
2
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A clothing store manager notices that when any one customer comes into the store, there is a 52% chance they will make a purchase. She also notices that one customer’s decision to make a purchase is independent of other customers’ decisions. Suppose one Friday, 75 customers come into this store. Let X represent the number of customers who make a purchase.What is the shape of the probability histogram of X?

A
skewed left
B
skewed right
C
approximately uniform
D
approximately symmetric
3

Tropical islands have many rainstorms during the afternoon heat. One particular tropical island has a 79% chance of a rainstorm on any given afternoon. Abraham is planning a weeklong stay on this tropical island. Let X represent the number of days there is an afternoon tropical storm that week. What are the mean and standard deviation of X?

A
Mu Subscript x Baseline = 1.47, Sigma Subscript x Baseline = 1.16
Option A
B
Mu Subscript x Baseline = 3.5, Sigma Subscript x Baseline = 1.16
Option B
C
Mu Subscript x Baseline = 5.53, Sigma Subscript x Baseline = 1.08
Option C
D
Mu Subscript x Baseline = 7, Sigma Subscript x Baseline = 3.5
Option D
4

Consider the given probability histogram of a binomial random variable.

Question illustration
A
Center: 2Shape: symmetric
B
Center: 2.5Shape: symmetric
C
Center: 2.5Shape: slightly skewed
D
Center: 3Shape: uniform
5

Ian shuffles a standard deck of 52 playing cards and turns over the first four cards, one at a time. He records the number of aces he observes.Have the conditions for a binomial setting been met for this scenario?

A
Yes, a success is “ace.”
B
Yes, all four conditions in BINS have been met.
C
No, we do not know how many aces will occur in those first four cards.
D
No, the cards are not being replaced, so the independence condition is not met.
6

A fair coin is flipped three times, and the number of times it comes up "heads” is recorded.Have the conditions for a binomial setting been met for this scenario?

A
No, this is a fair coin.
B
Yes, all four conditions in BINS have been met.
C
No, the coin flips are not independent of one another.
D
No, the coin needs to be flipped until “heads” appears. The number of trials needed to get “heads” should be recorded.
7

A spinner is divided into six equal-sized sectors labeled 1 through 6. Dwayne spins this spinner 12 times. Let X represent the number of 1s that are spun. What are the mean and standard deviation of X?

A
Mu Subscript x Baseline = 1, Sigma Subscript x Baseline = 1.29
Option A
B
Mu Subscript x Baseline = 2, Sigma Subscript x Baseline = 1.29
Option B
C
Mu Subscript x Baseline = 2, Sigma Subscript x Baseline = 1.67
Option C
D
Mu Subscript x Baseline = 10, Sigma Subscript x Baseline = 2.78
Option D
8

The probability of an archer hitting her target is 83%. Suppose she has 20 shots to take, and each shot is independent of the others. Let X represent the number of targets hit. What is the mean of X?

A
4.1
B
8.3
C
16.6
D
83
9

A coin is weighted so that the probability of getting heads is . Suppose you toss this coin 15 times. Let X represent the number of heads. What are the mean and standard deviation of X?

Question illustration
A
Mu Subscript x Baseline = 0.67, Sigma Subscript x Baseline = 0.88
Option A
B
Mu Subscript x Baseline = 7.5, Sigma Subscript x Baseline = 2.33
Option B
C
Mu Subscript x Baseline = 7.5, Sigma Subscript x Baseline = 3.33
Option C
D
Mu Subscript x Baseline = 10, Sigma Subscript x Baseline = 1.83
Option D
10

There are 10 multiple-choice questions on a math quiz. Each question has four answer choices with one correct answer. Let X represent the number of questions answered correctly for a student who is randomly guessing each answer choice.Have the conditions for a binomial setting been met for this scenario?

A
No, the order of the questions is unknown.
B
Yes, all four conditions in BINS have been met.
C
No, the answers are not independent of one another.
D
No, we do not know how many quizzes this teacher will give.

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