Question

Seventy-six percent of sunflower seeds will germinate into a flower, and a sample of 800 such sunflower seeds is randomly selected. The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:

Answer 1

12.08

Explanation:

For each sunflower, there are only two possible outcomes. Either it germinates, or it does not. The probability of a sunflower germinating is independent of other sunflowers. 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 standard deviation of the binomial distribution is:

`√(V(X)) = √(np(1-p))`

Seventy-six percent of sunflower seeds will germinate into a flower

This means that
`p = 0.76`

Samples of 800:

This means that
`n = 800`

The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:

`√(V(X)) = √(np(1-p)) = √(800*0.76*0.24) = 12.08`