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

Answer:

12.08

Step-by-step 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:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

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:

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.76*0.24} = 12.08$