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

Chemical signals of mice.Consider 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 theThe 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. Explain why the probability distribution of x can be ­approximated by the binomial distribution. Find E(x) and interpret its value, practically. Find the variance of x. Give an interval that is likely to contain the value of x.

Solutions

Expert Solution

the binomial distribution has three main characteristics

1. each trial results in two outcomes SUCCESS and FAILURE.

2. each trial can be repeated under identical conditions.

3. the total no. trials is fixed.

In this case all this characteristics are satisfied, as

in each mice cell either it responds positively or not - so in each trial there are exactly two outcomes success and failure.

the mouse cells are all identical - so each trial is repeated in identical conditions.

total mouse cell in the sample =100 - so the sample size is fixed.

Let x represent the number of cells that respond positively.Then  the probability distribution of x can be ­approximated by the binomial distribution.

40% of the lab mice cells responded positively,

we know for   

interpretation; out of 100 mice cells it is expected that 40 of them will repond positively.

the interval which is likely to contain the value of X is,


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