QUESTIONS
Question 1
A random sample of college students majoring in cinematography were surveyed about their movie habits. One question in the survey asked, “How many documentaries have you watched in the past month?” The table below represents the probability density function for the random variable X, the number of documentaries watched by cinematography majors in the past month. Find the standard deviation of X.
- Round the final answer to two decimal places.
| x | P(X = x) |
| 4 | 1/5 |
| 6 | 2/5 |
| 8 | 2/5 |
Question 2
The table below shows a probability density function for the discrete random variable X, the number of extra credit points students received on a statistics final exam. What is the probability that X is 1, 2, or 4?
- Provide the final answer as a fraction.
| x | P(X = x) |
| 0 | 3/20 |
| 1 | 1/20 |
| 2 | 7/20 |
| 3 | 3/10 |
| 4 | 1/10 |
| 5 | 1/20 |
Question 3
Which of the following tables shows a valid probability density function? Select all correct answers.
| x | P(X=x) |
| 0 | 0.6 |
| 1 | 0.01 |
| 2 | 0.14 |
| x | P(X=x) |
| 0 | 310 |
| 1 | 110 |
| 2 | 25 |
| x | P(X=x) |
| 0 | 18 |
| 1 | 14 |
| 2 | 58 |
| x | P(X=x) |
| 0 | 0.13 |
| 1 | 0.09 |
| 2 | 0.45 |
| 3 | 0.27 |
| 4 | 0.06 |
| x | P(X=x) |
| 0 | −15 |
| 1 | 310 |
| 2 | 12 |
| 3 | 310 |
| 4 | 110 |
| x | P(X=x) |
| 0 | 12 |
| 1 | 18 |
| 2 | 38 |
Question 4
A casino features a game in which a weighted coin is tossed several times. The table shows the probability of each payout amount (assume that the remaining probability has a payout of 0 so that the probabilities add to 1). To the nearest dollar, what is expected payout of the game?
| Payout Amount | $130 | $4,400 | $195,000 |
| Probability | 0.156 | 0.023 | 0.0007 |
Question 5
A casino features a game in which a weighted coin is tossed several times. The table shows the probability of each payout amount (assume that the remaining probability has a payout of 0 so that the probabilities add to 1). To the nearest dollar, what is expected payout of the game?
| Payout Amount | $130 | $2,800 | $135,000 |
| Probability | 0.131 | 0.021 | 0.0003 |
Question 6
During a college football national championship, the number of times football teams scored a touchdown was recorded by a scorekeeper every quarter. The table below represents the probability density function for the random variable X, the number of touchdowns per quarter. Find the standard deviation of X.
- Round the final answer to two decimal places.
| x | P(X = x) |
| 1 | 1/5 |
| 2 | 1/5 |
| 8 | 1/5 |
| 9 | 2/5 |
Question 7
Which of the following tables shows a valid probability density function? Select all correct answers.
| x | P(X=x) |
| 0 | 14 |
| 1 | 12 |
| 2 | 14 |
| x | P(X=x) |
| 0 | 12 |
| 1 | 18 |
| 2 | 14 |
| 3 | 18 |
| x | P(X=x) |
| 0 | 0.0 |
| 1 | 0.02 |
| 2 | 0.16 |
| 3 | 0.0 |
| 4 | 1.07 |
| x | P(X=x) |
| 0 | 0.89 |
| 1 | 0.09 |
| 2 | 0.0 |
| 3 | 0.02 |
| 4 | 0.0 |
| x | P(X=x) |
| 0 | 35 |
| 1 | 25 |
| 2 | −110 |
| 3 | 110 |
| x | P(X=x) |
| 0 | 110 |
| 1 | 110 |
| 2 | 310 |
| 3 | 310 |
Question 8
Which of the following tables shows a valid probability density function? Select all correct answers.
| x | P(X=x) |
| 0 | 38 |
| 1 | 14 |
| 2 | 38 |
| x | P(X=x) |
| 0 | 0.2 |
| 1 | 0.1 |
| 2 | 0.35 |
| 3 | 0.17 |
| x | P(X=x) |
| 0 | 910 |
| 1 | −310 |
| 2 | 310 |
| 3 | 110 |
| x | P(X=x) |
| 0 | 0.06 |
| 1 | 0.01 |
| 2 | 0.07 |
| 3 | 0.86 |
| x | P(X=x) |
| 0 | 12 |
| 1 | 18 |
| 2 | 14 |
| 3 | 18 |
| x | P(X=x) |
| 0 | 110 |
| 1 | 110 |
| 2 | 310 |
| 3 | 15 |
Question 9
Which of the following tables shows a valid probability density function? Select all correct answers.
| x | P(X=x) |
| 0 | 0.06 |
| 1 | 0.01 |
| 2 | 0.0 |
| 3 | 0.66 |
| 4 | 0.01 |
| x | P(X=x) |
| 0 | 0.07 |
| 1 | 0.23 |
| 2 | 0.02 |
| 3 | 0.13 |
| 4 | 0.55 |
| x | P(X=x) |
| 0 | 14 |
| 1 | 12 |
| 2 | 14 |
| x | P(X=x) |
| 0 | 38 |
| 1 | 14 |
| 2 | 18 |
| 3 | 14 |
| x | P(X=x) |
| 0 | 15 |
| 1 | 12 |
| 2 | 25 |
| 3 | 110 |
| 4 | −15 |
| x | P(X=x) |
| 0 | 15 |
| 1 | 310 |
| 2 | 110 |
| 3 | 110 |
Question 10
A player can play a game by rolling a fair die several times. The player can win money based on the numbers rolled. The table shows the probability of each payout amount (assume that the remaining probability has a payout of 0 so that the probabilities add to 1). To the nearest dollar, what is the expected payout of the game?
| Payout Amount | $160 | $4,800 | $195,000 |
| Probability | 0.116 | 0.028 | 0.0005 |
Question 11
A gambling game involves a spinner with the numbers 1 through 25. To play, the player guesses which numbers the spinner will land on. The table shows the probability of each payout amount (assume that the remaining probability has a payout of 0 so that the probabilities add to 1). To the nearest dollar, what is the expected payout of the game?
| Payout Amount | $140 | $4,400 | $170,000 |
| Probability | 0.116 | 0.021 | 0.0007 |
Question 12
Andrew is a quality control inspector at a clothing factory. At the end of each day, he checks the number of imperfections found in cotton sweaters. The table below represents the probability density function for the random variable X, the number of imperfections found in cotton sweaters per day. Find the standard deviation of X.
- Round the final answer to two decimal places.
| x | P(X = x) |
| 0 | 1/6 |
| 1 | 1/6 |
| 4 | 1/3 |
| 7 | 1/3 |
Question 13
A random sample of high school students were surveyed about technological devices. They were asked, “How many computers do you have in your household?” The table below represents the probability density function for the random variable X, the number of computers per household. Find the standard deviation of X.
- Round the final answer to two decimal places.
| x | P(X = x) |
| 3 | 1/4 |
| 4 | 1/4 |
| 7 | 1/2 |
ANSWERS:
Question 1
A random sample of college students majoring in cinematography were surveyed about their movie habits. One question in the survey asked, “How many documentaries have you watched in the past month?” The table below represents the probability density function for the random variable X, the number of documentaries watched by cinematography majors in the past month. Find the standard deviation of X.
- Round the final answer to two decimal places.
| x | P(X = x) |
| 4 | 1/5 |
| 6 | 2/5 |
| 8 | 2/5 |
Answer:
Std = 1.50 documentaries
A filled out table.
| X | P(X-x) | x.P(X-x) | (x-µ)2.P(X-x) |
| 4 | 1/5 | 4/5 | 1.152 |
| 6 | 2/5 | 12/5 | 0.064 |
| 8 | 2/5 | 16/5 | 1.024 |
Question 2
The table below shows a probability density function for the discrete random variable X, the number of extra credit points students received on a statistics final exam. What is the probability that X is 1, 2, or 4?
- Provide the final answer as a fraction.
| x | P(X = x) |
| 0 | 3/20 |
| 1 | 1/20 |
| 2 | 7/20 |
| 3 | 3/10 |
| 4 | 1/10 |
| 5 | 1/20 |
Answer
1/2
Question 3
Which of the following tables shows a valid probability density function? Select all correct answers.
| x | P(X=x) |
| 0 | 0.6 |
| 1 | 0.01 |
| 2 | 0.14 |
| x | P(X=x) |
| 0 | 310 |
| 1 | 110 |
| 2 | 25 |
| x | P(X=x) |
| 0 | 18 |
| 1 | 14 |
| 2 | 58 |
| x | P(X=x) |
| 0 | 0.13 |
| 1 | 0.09 |
| 2 | 0.45 |
| 3 | 0.27 |
| 4 | 0.06 |
| x | P(X=x) |
| 0 | −15 |
| 1 | 310 |
| 2 | 12 |
| 3 | 310 |
| 4 | 110 |
| x | P(X=x) |
| 0 | 12 |
| 1 | 18 |
| 2 | 38 |
Answer
| x | P(X=x) |
| 0 | 18 |
| 1 | 14 |
| 2 | 58 |
|
x |
P(X=x) |
| 0 | 0.13 |
| 1 | 0.09 |
| 2 | 0.45 |
| 3 | 0.27 |
| 4 | 0.06 |
|
x |
P(X=x) |
| 0 | 12 |
| 1 | 18 |
| 2 | 38 |
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