**In the following probability distribution, the random variable x represents the number of activities a…**

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## Question “In the following probability distribution, the random variable x represents the number of activities a…”

In the following probability distribution, the random variable x represents the number of activities a parent of a 6 th- to 8th-grade student is involved in. Complete parts (a) through (f) below.

x | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|

P(x) | 0.367 | 0.133 | 0.209 | 0.116 | 0.175 |

(a) Verify that this is a discrete probability distribution.

This is a discrete probability distribution because the sum of the probabilities is _______ and each probability is _______

(b) Graph the discrete probability distribution. Choose the correct graph below.

(c) Compute and interpret the mean of the random variable x .

The mean is _______ activities.

(Type an integer or a decimal. Do not round.)

Which of the following interpretations of the mean is correct?

A. The observed value of an experiment will be less than the mean of the random variable in most experiments.

B. The observed value of an experiment will be equal to the mean of the random variable in most experiments.

C. As the number of experiments decreases, the mean of the observations will approach the mean of the random variable.

D. As the number of experiments increases, the mean of the observations will approach the mean of the random variable.

(d) Compute the standard deviation of the random variable x.

The standard deviation is _______ activities.

(Round to one decimal place as needed.)

(e) What is the probability that a randomly selected student has a parent involved in three activities?

The probability is

(Type an integer or a decimal. Do not round.)

(f) What is the probability that a randomly selected student has a parent involved in three or four activities?

The probability is

(Type an integer or a decimal. Do not round.)

## Answer

(C)

(D)

## Conclusion

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