63 Chemical signals of mice. Cell (May 14, 2010) conducted a study of the ability of a mouse to recognize the odor of a potential predator. 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 .