Question

In an? experiment, 32 ?% 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 200 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 are

nothing

identical trials. For each? trial, there

?

are two

are many

is one

possible? outcome(s). The probability of each possible outcome

?

is different

is the same

for each? trial, and the trials are all

?

independent.

related.

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

?E(x)equals

nothing

?(Round to the nearest whole number as? needed.)

Interpret this value. Choose the correct answer below.

A.

Exactly? E(x) cells out of

200

will respond positively in similar experiments.

B.

On average? E(x) cells out of

200

will respond positively in similar experiments.

C.

At most? E(x) cells out of

200

will respond positively in similar experiments.

D.

At least? E(x) cells out of

200

will respond positively in similar experiments.

c. Find the variance of x.

The variance of x is

nothing

.

?(Round to two decimal places as? needed.)

d. Give an interval that is? 95% likely to contain the value of x.

Using the empirical? rule, x is likely in the interval

?(nothing

?,nothing

?).

?(Round to one decimal place as? needed.)

Answer 1

A bit theory

Here by the problem,

In an experiment, 32% of lab mice cells exposed to chemically produced cat Mups responded positively. Now we consider a sample of n=200 lab mice cells, each exposed to chemically produced cat Mups.

Now let X represent the number of cells that respond positively.

a. Now from the theory given, the probability distribution of X can be approximated by the binomial distribution.

There are n=200 identical trials. For each trial, there are two possible outcomes. The probability of each possible outcome is the same for each trial, and the trials are all independent

b. Now the expected value of X be, where X~Binomial(200,0.32)

Interpretation:

On average 64 cells out of 200 will respond positively in similar experiments.

Hence option B is the correct one.

c. Now, the variance of X is

d. Now the interval 95% likely to contain the value of X using the empirical rule, where by empirical rule X ~Normal(64,43.52) is,

where be the upper 0.025 point of standard normal distribution

So the interval be,

Hence the answer................

Thank you...............