Question

The ability of a mouse to recognize the odor of a potential predator is essential to the mouse’s survival. Typically, the source of these odors are major urinary proteins (Mups). 30% of lab mice sells 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 represents 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 (2 st. dev around the mean).

e) How likely is it that less than half of the cells respond positively to cat Mups?

Answer 1

a)

as number of trails n=100 are fixed; probability of event p=0.30 is fixed and independent from trail to trail and there is only two outcomes exposed and unexposed,hence it is binomial distribution

b)

here mean of distribution=μ=np=

30

this tells that if a large number of samples of size 100 is taken then on average 30 mice per sample will get exposed to  chemically produced cat Mups responded positively

c)

and standard deviation σ=sqrt(np(1-p))=

4.5826

this tells that  if a large number of samples of size 100 is taken then average deviation from population mean will be 4.58 mice in a sample,

d)

minimum usual value =μ-2*σ =		20.83
maximum usual value =μ-2*σ =		39.17

e)

as our usual values interval has all value below half of the cells ; thereore it is highly likely that   less than half of the cells respond positively to cat Mups

probability of above event is approximatey 1,