Answer:
The mean of X is 122.5 and the standard deviation is 7.9.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they believe that the overall state of moral values is poor, or they do not believe this. The probability of an adult believing this is independent of other adults. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

In this problem, we have that:

So


The mean of X is 122.5 and the standard deviation is 7.9.
The 4 in 42,672 is 40,000
And the 4 in 37,426 is 400
The answer is 100
7th grade has 3 boy out of 10 students
probability of picking a boy is 3/10
8th grade has 9 boys out of 12 students are boys
probability of picking a boy is 9/12 reduced to 3/4
3/10 x 3/4 = 9/40 probability of picking 2 boys