Chemical signals of mice. Refer to the Cell(May 14, 2010) study of the ability of a mouse...

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

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b. Find E(x) and interpret its value, practically.

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c. Find the variance of x.

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d. Give an interval that is likely to contain the value of x.

Chemical signals of mice. The ability of a mouse to recognize the odor of a potential predator (e.g., a cat) is essential to the mouse’s survival. The chemical makeup of theseodors—called kairomones—was the subject of a studypublished in Cell(May 14, 2010). Typically, the source of these odors are major urinary proteins (Mups). Cells collected from lab mice were exposed to Mups from rodent species A, Mups from rodent species B, and kairomones (from a cat). The accompanying Venn diagram shows the proportion of cells that chemically responded to each of the three odors. (Note: A cell may respond to more than a single odor.)

a. What is the probability that a lab mouse responds to all three source odors?

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b. What is the probability that a lab mouse responds to the kairomone?

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c. What is the probability that a lab mouse responds to Mups A and Mups B, but not the kairomone?