Question

# In the following probability​ distribution, the random variable x represents the number of activities a parent...

In the following probability​ distribution, the random variable x represents the number of activities a parent of a

6th to 8th​-grade student is involved in. Complete parts​ (a) through​ (f) below.

 x ​P(x) 0 1 2 3 4 0.395 0.075 0.199 0.195 0.136

​(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 ___ (Less than or equal to 1; Greater than or equal to 0; Between 0 and 1 inclusive; Greater than 0 and less than 1)

​(b) Graph the discrete probability distribution.

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

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

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

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

(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.)