1. Which random variable is a binomial random variable? A. X = the number of pho

Question

1. Which random variable is a binomial random variable?
A. X = the number of phone calls received in a one-hour period.
B. A fair die is rolled seven times. Let X = the number of times wesee an even number.
C. A fair coin is flipped multiple times. Let X = the number oftimes the coin needs to be flipped until we see ten tails.
D. There are ten people in the room: five men and five women. Threepeople are to be selected at random to form a committee. Let X =the number of men on the three-person committee.

2. A set of ten cards consists of five red cards and five blackcards. The cards are shuffled thoroughly. Four of these cards willbe selected at random without replacement. Let X = the number ofred card in the set of four selected cards. Which of the followingprobability distributions is appropriate for the random variableX?
A. The normal distribution with mean 3 and variance 1.22.
B. The binomial distribution with parameters n = 4 and p = 0.5.
C. The binomial distribution with parameters n = 10 and p =0.5.
D. The binomial distribution is inappropriate because the resultsof trials are not independent.

3. A set of ten cards consists of five red cards and five blackcards. The cards are shuffled thoroughly. Four of these cards willbe selected at random with replacement. Let X = the number of redcard in the set of Four selected cards. Which of the followingprobability distributions is appropriate for the random variableX?
A. The normal distribution with mean 3 and variance 1.22.
B. The binomial distribution with parameters n = 4 and p = 0.5.
C. The binomial distribution with parameters n = 10 and p =0.5.
D. The binomial distribution is inappropriate because the resultsof trials are not independent.

4. A balanced die is rolled 12 times. Let X = the number of timeswe see an even number. What is the appropriate distribution for therandom variable X?
A. Not a binomial distribution.
B. A normal distribution with 6 trials and probability of success1/6
C. B(12, 1/2) ( a binomial distribution with 12 trials andprobability of success 1/2 ).
D. B( 12, 1/6) ( a normal distribution with 12 trials andprobability of success 1/6 ).

5. A multiple choice quiz consists of 8 questions, each with 5possible answers. If a student randomly guesses an answer to eachquestion, what is the probability that the student get exactly 2correct answers? (Use the Binomial Table)
A. 0.29
B. 0.71
C. 0.53
D. 0.83

(Hint: Think about the connection and difference between questions6, 7, 8 and 9).

6. A college basketball player is known to miss 20% of his freethrows. At the end of a game, the team is losing by two points. Heis fouled attempting a three-point shot and is awarded three freethrows. Assuming each free throw is independent, what is theprobability that he misses exactly one of these throws? (Use theBinomial Table)
A. 0.384
B. 0.80
C. 0.64
D. 0.896

7. A college basketball player is known to make 80% of his freethrows. At the end of a game, the team is losing by two points. Heis fouled attempting a three-point shot and is awarded three freethrows. Assuming each free throw is independent, what is theprobability that he makes exactly two throws? (Use the BinomialTable)
A. 0.384
B. 0.80
C. 0.64
D. 0.896

8. A college basketball player is known to make 80% of his freethrows. At the end of a game, the team is losing by two points. Heis fouled attempting a three-point shot and is awarded three freethrows. Assuming each free throw is independent, what is theprobability that he makes at least two of these throws?
A. 0.384
B. 0.80
C. 0.64
D. 0.896

9. A college basketball player is known to miss 20% of his freethrows. At the end of a game, the team is losing by two points. Heis fouled attempting a three-point shot and is awarded three freethrows. Assuming each free throw is independent, what is theprobability that he misses no more than one of these throws?
A. 0.384
B. 0.80
C. 0.64
D. 0.896

10. A multiple choice quiz consists of 7 questions, each with 5possible answers. If a student guesses answer to each question,then the mean (expected) number of correct answers is
A. 7.00
B. 1.40
C. 5.00
D. 12.00

Explanation / Answer

1. Which random variable is a binomial random variable? A. X = the number of phone calls received in a one-hour period. B. A fair die is rolledseven times. Let X = the number of times we see an evennumber. C. A fair coin is flipped multiple times. Let X =the number of times the coin needs to be flipped until we see tentails. D. There are ten people in the room: five men and five women. Threepeople are to be selected at random to form a committee. Let X =the number of men on the three-person committee. 2. A set of ten cards consists of five red cards and five blackcards. The cards are shuffled thoroughly. Four of these cards willbe selected at random without replacement. Let X = the number ofred card in the set of four selected cards. Which of the followingprobability distributions is appropriate for the random variableX? A. The normal distribution with mean 3 and variance 1.22. B. The binomial distribution with parameters n = 4 and p = 0.5. C. The binomial distribution with parameters n = 10 and p =0.5. D. The binomial distributionis inappropriate because the results of trials are notindependent. 3. A set of ten cards consists of five red cards and five blackcards. The cards are shuffled thoroughly. Four of these cards willbe selected at random with replacement. Let X = the number of redcard in the set of Four selected cards. Which of the followingprobability distributions is appropriate for the random variableX? A. The normal distribution with mean 3 and variance 1.22. B. The binomial distributionwith parameters n = 4 and p = 0.5. C. The binomialdistribution with parameters n = 10 and p = 0.5. D. The binomial distribution is inappropriate because the resultsof trials are not independent. 4. A balanced die is rolled 12 times. Let X = the number of timeswe see an even number. What is the appropriate distribution for therandom variable X? A. Not a binomial distribution. B. A normal distribution with 6 trials and probability of success1/6 C. B(12, 1/2) ( a binomialdistribution with 12 trials and probability of success 1/2). D. B( 12, 1/6) ( a normal distribution with 12 trialsand probability of success 1/6 ). 5. A multiple choice quiz consists of 8 questions, each with 5possible answers. If a student randomly guesses an answer to eachquestion, what is the probability that the student get exactly 2correct answers? (Use the Binomial Table) A. 0.29 B.0.71 C. 0.53 D. 0.83 (Hint: Think about the connection and difference between questions6, 7, 8 and 9). 6. A college basketball player is known to miss 20% of his freethrows. At the end of a game, the team is losing by two points. Heis fouled attempting a three-point shot and is awarded three freethrows. Assuming each free throw is independent, what is theprobability that he misses exactly one of these throws? (Use theBinomial Table) A. 0.384 B.0.80 C. 0.64 D. 0.896 7. A college basketball player is known to make 80% of his freethrows. At the end of a game, the team is losing by two points. Heis fouled attempting a three-point shot and is awarded three freethrows. Assuming each free throw is independent, what is theprobability that he makes exactly two throws? (Use the BinomialTable) A. 0.384 B. 0.80 C. 0.64 D. 0.896 8. A college basketball player is known to make 80% of his freethrows. At the end of a game, the team is losing by two points. Heis fouled attempting a three-point shot and is awarded three freethrows. Assuming each free throw is independent, what is theprobability that he makes at least two of these throws? A. 0.384 B. 0.80 C. 0.64 D. 0.896 9. A college basketball player is known to miss 20% of his freethrows. At the end of a game, the team is losing by two points. Heis fouled attempting a three-point shot and is awarded three freethrows. Assuming each free throw is independent, what is theprobability that he misses no more than one of these throws? A. 0.384 B. 0.80 C. 0.64 D. 0.896 10. A multiple choice quiz consists of 7 questions, each with 5possible answers. If a student guesses answer to each question,then the mean (expected) number of correct answers is A. 7.00 B. 1.40 C.5.00 D. 12.00

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