Question

In an experiment, 44% of lab mice cells exposed to chemically produced cat Mups responded positively (ie recognized the danger of the lurking predator Consider a sample of 50 lab mice cells, each exposed to chemically produced cat Mups. Let x represent the number of cells that respond positively. Complete parts a through d below. a. Explain why the probability distribution of x can be approximated by the binomial distribution. There areidentical trials. For each trial, there are all b. Find E(x) and interpret its value, practically.are two possible outcome(s). The probability of each possible outcome for each trial, and the trials are many related. is one independent. is different is the same E-(Round to the nearest whole number as needed.) Interpret this value. Choose the correct answer below. O A. O B. O C. O D. At most E(x) cells out of 50 will respond positively in similar experiments. On average E(x) cells out of 50 will respond positively in similar experiments. Exactly E(x) cells out of 50 will respond positively in similar experiments. At least E(x) cells out of 50 will respond positively in similar experiments.

Answer 1

Let X denote the number of cells that respond positively. Then, $X\sim Bin(n=50,p=0.44)$

a)

There are 50 identical trials. For each trial, there are two possible outcomes. The probability of each possible outcome is the same, and the trials are all independent.

So, X can be approximated by Binomial distribution.

b)

We know that for Binomial distribution, E(X) = np = 50(0.44) = 22

So, on average E(X) cells out of 50 will respond positively in similar experiments.

Hence option B is the correct option.

c)

We know that for Binomial distribution, Var(X) = np(1-p) = 50(0.44)(1-0.44) = 12.32

d)

From the empirical rule, we know that 95% observations lie within 2 Standard deviations from the mean. So, 95% observations would probably lie in the interval:

$(E(X)-2\sqrt{Var(X)},E(X)+2\sqrt{Var(X)})$

$(22-2\sqrt{12.32},22+2\sqrt{12.32})$

$(15.0,29.0)$