## Related questions with answers

In an attempt to increase sales, a breakfast cereal company decides to offer a promotion. Each box of cereal will contain a collectible card featuring one NASCAR driver: Kyle Busch; Dale Earnhardt, Jr.; Kasey Kahne; Danica Patrick; or Jimmie Johnson. The company says that each of the 5 cards is equally likely to appear in the 100,000 boxes of cereal that are part of this promotion. You buy 12 boxes and let X = the number of Kyle Busch cards in the sample. Calculate the mean and standard deviation of the sampling distribution of X.

Solution

VerifiedWe know that if $X$ is the number of successes in a random sample of size $n$ from a large population with a proportion of successes $p$. Then,

The $\textbf{mean}$ of the sampling distribution of $X$ is given by $\mu=np$.

The $\textbf{standard deviation}$ of the sampling distribution of $X$ is given by formula $\sigma=\sqrt{np(1-p)}$.

Here, it is given that all the five cards in the box are equally likely to appear in the 100,000 boxes of cereal that are part of this promotion. If we buy 12 boxes and let $X$ be the number of Kyle Busch cards in the sample.

The size of the sample is given as $n=12$ and the proportion of success that a Kyle Busch card is selected out of five cards is $\dfrac{1}{5}$ means $p=0.2$.

Thus, by applying the formula stated above, we could say that the mean of the sample distribution of $X$ is

$\mu_X=np=12\times 0.2=2.4$

and the standard deviation of the sample distribution of $X$ is

$\sigma_X=\sqrt{np(1-p)}=\sqrt{2.4(1-0.2)}=\sqrt{2.4\times 0.8}=\sqrt{1.92}\approx 1.39$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Probability and Statistical Inference

10th Edition•ISBN: 9780135189399Dale Zimmerman, Elliot Tanis, Robert V. Hogg#### Probability and Statistics for Engineering and the Sciences

8th Edition•ISBN: 9780538733526 (4 more)Jay L. Devore#### Probability and Statistics for Engineering and the Sciences

9th Edition•ISBN: 9781305251809 (9 more)Jay L. Devore#### Statistics and Probability with Applications

3rd Edition•ISBN: 9781464122163Daren S. Starnes, Josh Tabor## More related questions

1/4

1/7