Refer to the Cell (May 14, 2010) study of the ability of a mouse to recognize the odor of a potential predator, Exercise 3.63 (p. 143). Recall that the sources of these odors are typically major urinary proteins (Mups). In an experiment, 40% of lab mice cells exposed to chemically produced cat Mups responded positively (i.e., recognized the danger of the lurking predator). Consider a sample of 100 lab mice cells, each exposed to chemically produced cat Mups. Let x represent the number of cells that respond positively.

a. Explain why the probability distribution of x can be approximated 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.