Question

Previous research suggests that 1 of every 8 students happens to be in a sports team. A research assistant (RA) randomly surveys 16 students from a university and asks if they are in a sports team.

(a) Is this an example of a binomial experiment? Why or why not?

(b) What is the probability that the RA finds none of the 16 students are in a sports team?

(c) What is the probability that the RA finds at least 1 student is in a sports team?

(d) Find the mean and standard deviation of the number of students in a sports team.

Answer 1

(a)

This is an example of a binomial experiment because:

n = Total number of trials = 16 is fixed

p = Probability of success = 1/8 = 0.125 is constant in all trials

The trials are independent.

(b)

So,

Answer is:

0.1181

(c)

P(X1) = 1 - P(X=0) = 1 - 0.1181 =0.8819

So,

Answer is:

0.8819

(d)

(i) mean = np = 16 X 0.125 = 2

So,

Answer is:

2

(ii) Standard Deviation =

So,

Answer is:

1.3229