Question

Consider a binomial experiment. If the number of trials is increased, what happens to the expected value? To the standard deviation? Explain.

WRITE IN TEXT NOT IMAGE TEXT SINCE I CANT READ SOME OF THE HANDWRITING IN IMAGE TEXT

Answer 1

we know that mean and standard deviation of binomial distribution are given as

Mean = n*p

and

Standard deviation =

where n is the number of trails and p is the probability

We can see that the mean and standard deviation are directly proportional to the number of trails n. This means that if we increase the number of trials, then mean and standard deviation will also increase and if we decrease the number of trials, then the mean and standard deviation will also decrease

For example

consider a binomial experiment with n = 50 and p =0.10

then

mean = n*p = 50*0.10 = 5

and SD = sqrt(n*p*(1-p)) = sqrt(50*0.10*(1-0.10)) = 2.12

and if we increase the number of trial n to 100, then

mean = n*p = 100*0.10 = 10

and SD = sqrt(n*p*(1-p)) = sqrt(100*0.10*(1-0.10)) = 3