Chapter 6 Quiz

1. In the following probability​ distribution, the random variable x represents the number of activities a parent of a K to 5th​-grade student is involved in. Complete parts​ (a) through​ (f) below.

(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?

1. The observed value of an experiment will be equal to the mean of the random variable in most experiments.
2. As the number of experiments​ decreases, the mean of the observations will approach the mean of the random variable.
3. The observed value of an experiment will be less than the mean of the random variable in most experiments.
4. 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 ____ 0.444.  ​(Type an integer or a decimal. Do not​ round.)

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P(4) = _____

3.  Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer.  An experimental drug is administered to 120 randomly selected​ individuals, with the number of individuals responding favorably recorded.  Does the probability experiment represent a binomial​ experiment?

1.  ​No, because there are more than two mutually exclusive outcomes for each trial. 
2. ​No, because the trials of the experiment are not independent. 
3. ​No, because the probability of success differs from trial to trial. 
4. ​Yes, because the experiment satisfies all the criteria for a binomial experiment.

4.  What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success​ p? 
Choose the correct forumla below.

$$\begin{gathered} A. E\left(X\right) = {(1–p)}^n {(1–p)}^n \\ B. E\left(X\right) = \sqrt{np(1–p)} \\ C. E\left(X\right) = p^n \\ D. E\left(X\right) = np \end{gathered}$$

5.  Determine whether the random variable is discrete or continuous. In each​ case, state the possible values of the random variable.
​(a) The number of customers arriving at a bank between noon and 1:00 P.M.
​(b) The .amount of snowfall

​(a) Is the number of  discrete or​ continuous?

1. The random variable is discrete. The possible values are
   $x\ge 0$
2. The random variable is continuous. The possible values are
   $x\ge 0$

   .

3. The random variable is discrete. The possible values are x=​0, ​1, ​2,…
4. The random variable is continuous. The possible values are x​=0, ​1, ​2,…

(b) Is the  discrete or​ continuous?

1. The random variable is continuous. The possible values are s=1,2,3…
2. The random variable is discrete. The possible values are s=1,2,3….
3. The random variable is discrete. The possible values are
   $s\ge 0$
4. The random variable is continuous. The possible values are 
   $s\ge 0$

   .

6. The following data represent the number of games played in each series of an annual tournament from 1929 to 2005 . Complete parts​ (a) through​ (d) below.

​(a) Construct a discrete probability distribution for the random variable x. 

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

7. A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 11, p=0.2,

The probability of  successes is 

.   ​(Round to four decimal places as​ needed.)