Question

Of all the students applying for undergraduate studies, 13% applied to Honors college. Consider a randomly selected sample of 1500 students applying for undergraduate studies. Since we can view this as 1500 independent Bernoulli trials, this will be considered a binomial experiment.

A)The mean of the binomial distribution is given by
B)The standard deviation of this distribution is given by:
C)What is the variance of this distribution?
D)Find the probability that from the sample of 1500 students, strictly less than 160 students applied to Honors college.
E)Find the probability that more than 200 students applied to Honors college

Answer 1

Explanation:

Given that X no of students applying for Honors college is binomial with n =1500 and p = 0.13

a) Mean = E(x) = np =
`1500(0.13)\\= 195`

b) Variance= npq =
`195(0.87)\\= 169.65`

Std dev =13.025

c) Var = 169.65

d) P(X<160)

=0.00261

e) P(X>200) = 1-F(200)=0.3336

`P(X=r) = 1500Cr (0.13)^r (0.87)^(155-r)`

is the formula used.