Question

When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 39 % of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 56 of the dragon eggs to incubate. Consider all the possible samples of 56 dragon eggs.

What is the mean number of yellow eggs in samples of 56 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 56?

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

variance =

Answer 1

Solution:
Given that
n= 56,
p = 0.39

We can calculate the mean, variance and standard deviation of yellow eggs in sample of 56 eggs as follows
Mean= np = 56× 0.39 = 21.84
Mean = 21.84
Variance = [ np (1-p) ]
= [ (56×0.39)(1-0.39) ]
= 13.3224
Variance = 13.3224
Standard deviation=✓variance
=✓13.3224
=3.65
Standard deviation= 3.65

Answer 2

When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 26% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 68 of the dragon eggs to incubate. Consider all the possible samples of 68 dragon eggs.

What is the mean number of yellow eggs in samples of 68 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 68?
(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 68?
(Remember to calculate the answer using at least 5 decimal places, then give answer correct to at least one decimal place.)
variance =