The ability of a mouse to recognize the odor of a potentialpredator is essential to the mouse’s survival. Typically, thesource of these odors are major urinary proteins (Mups). 30% of labmice sells exposed to chemically produced cat Mups respondedpositively (i.e. recognized the danger of the lurking predator).Consider a sample of 100 lab mice cells, each exposed to chemicallyproduced cat MUPS. Let X represents the number of cells thatrespond positively.
a) Explain why the probability distribution of X can beapproximated by the binomial distribution.
b) Find E(X) and interpret its value, practically.
c) Find the variance of X.
d) Give an interval that is likely to contain the value of X (2st. dev around the mean).
e) How likely is it that less than half of the cells respondpositively to cat Mups?
