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 =

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.