Chapter 9, Problem 1EA

Check the Court's calculation of 29 standard deviations as the difference between the expected number of Mexican-Americans and the number actually chosen.

To determine

To check: The court’s calculation of the provided 29 standard deviations as the difference between the expected number of Mexican-Americans and the number that has been chosen.

Answer to Problem 1EA

Solution: The court’s calculation of the number of standard deviation is correct.

Explanation of Solution

Given: The court’s calculation of the provided 29 standard deviations.

Explanation:

Consider the summary provided in the textbook.

The standard deviation for the binomial distribution is provided by the square root of the product of total number of the sample, which is 870 times of the probability to select a Mexican-American (0.791) times the probability to select a non-Mexican American, which is 0.209.

So, the standard deviation is,

$\sqrt{870\times 0.791\times 0.209}=11.992$

Hence, 29 standard deviations are provided as,

$11.992\times 29=347.768$

Also, the expected number of Mexican-Americans is 688.

Number to choose in actual is 339.

Difference is;

$\begin{array}{c}688-339=349\\ =12\times 29.08\end{array}$

So, the court’s calculation of the number of standard deviation is correct.

Conclusion: The court’s calculation of the number of standard deviation is correct.