Question

When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 18% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 60 of the dragon eggs to incubate. Consider all the possible samples of 60 dragon eggs.

What is the mean number of yellow eggs in samples of 60 eggs? (that is the same as asking for the expected value of the number of yellow eggs)

(Give answer correct to at least one decimal place.)

mean =



What is the standard deviation in the number of yellow eggs in samples of size 60?

(Give answer correct to at least one decimal place.)

standard deviation =



What is the variance in the number of yellow eggs in samples of size 60?

(Remember to calculate the answer using at least 5 decimal places, then give answer correct to at least one decimal place.)

variance =

Answer 1

A) 10.8

B) 3.0

C) 8.86

Explanation:

Given that 18% of the eggs are yellow, and the rest green

Probability of yellow = 0.18

Probability of green = 0.82

the mean number of yellow eggs in samples of 60 eggs will be

Mean = xp

Where x = 60

P = 0.18

Mean P = 60 × 0.18 = 10.8

Let's also calculate the mean of the green eggs

Mean = 0.72 × 60 = 43.2

The standard deviation in the number of yellow eggs in samples of size 60 will be :

Standard deviation = root(npq)

= root(60×0.18×0.82)

= 2.975

= 3.0

What is the variance in the number of yellow eggs in samples of size 60?

Variance = square of standard deviation

Variance = 2.975^2

= 8.85600

= 8.86