Question

. It has been reported that 65% of college students graduate in four years. Consider a random sample of 40 students, and let the random variable X be the number who graduate in four years.

1. Define the random variable X of the form x~B(n,p)

2. Find the probability that exactly 25 students will graduate in four years.

c. Find the prob. that at least 30 students will graduate in four years.

d. Find the probability that less than 20 students will graduate in 4 years.

.

2. In 2009 it was reported that 45% of all car accidents in Buffalo were alcohol related. Suppose we take a random sample of 200 car accidents in Buffalo and let X be the number which are alcohol related.

a. Define the random variable X of the form )

2. Find the probability that fewer than half (less than 100) were alcohol related.

3. Find the prob. that between 60 and 80, inclusive, were alcohol related.

4. Find the probability at least 90 were alcohol related.

Answer 1

Note: Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.

Solution:

Given:

p = 0.65

n = 40

a)

Here, X follows Binomial distribution with n = 40 and p = 0.65

That is X follows B(40, 0.65)

b)

We have to find P(X=25) = ...?

Using binomial probability formula,

Therefore,

c)

We have to find P(X30) = ...?

Using excel formula,

=1-BINOMDIST(29,40,0.65,TRUE)

P(X30) = 0.1215

d)

We have to find P(X<20) = ...?

P(X<20) = P(X19)

Using excel function,

=BINOMDIST(19,40,0.65,TRUE)

P(X<20) = 0.0173

Done