Question

Finding and interpreting mean, variance, and standard deviation. Find the mean, variance, and standard deviation of the binomial distribution for the given random variable, and interpret the results.

Fifty-nine percent of likely US voters think that most school textbooks put political correctness ahead of accuracy. You randomly select seven likely US voters and ask them whether they think that most school textbooks put political correctness ahead of accuracy. the random variable represents the number of likely US voters who think that most school textbooks put political correctness ahead of accuracy.

Answer 1

1. 4.13

2. 1.6933

3. 1.3013

Explanation:

We have

Probability to be equal to 59% = 0.59

Sample size = n = 7 likely US voters

1. The mean:

= np

= Sample size x probability

= 7 x 0.59

= 4.13

2. The variance = nap

n = sample size

q = 1-probability = 1-0.59 = 0.41

P = probability = 0.59

Variance = 7x0.59x0.41

= 1.6933

3. Standard deviation

= Square root of variance

√1.6933

= 1.3013

A mean of 4.13, indicates that 4 of these voters put political correctness ahead on the average.