Problem 6CRE

Investing in College Based on a USA Today poll, assume that 10% of the population believes that college is no longer a good investment.

a. Find the probability that among 16 randomly selected people, exactly 4 believe that college is no longer a good investment.

b. Find the probability that among 16 randomly selected people, at least 1 believes that college is no longer a good investment.

c. The poll results were obtained by Internet users logged on to the USA Today Web site, and the Internet users decided whether to ignore the posted survey or respond. What type of sample is this? What does it suggest about the validity of the results?

Problem 6CRE

Answer:

Step1 of 1:

We have Based on a USA Today poll, assume that 10% of the population believes that college is no longer a good investment.that is p = 0.10.

Consider a random variable “x” follows binomial distribution with sample size “n” and proportion “p”.

i,e.X B(n, p)

Where,

n = 16 and p = 0.10.

q = 1 - p

= 1 - 0.10

= 0.90.

Probability mass function of binomial distribution is given by

P(x) = , x = 0,1,2,...,n.

a).

The probability that among 16 randomly selected people, exactly 4 believe that college is no longer a good investment is given by

P(x) =

P(x = 4) =

= 18200.00010.2824

= 0.0514

Therefore,The probability that among 16 randomly selected people, exactly 4 believe that college is no longer a good investment is 0.0514.

b).

The probability that among 16 randomly selected people, at least 1 believes that college is no longer a good investment is given by

P(x) =

P(x 1) = 1 - P(x 0)

= 1 -

= 1 - (110.1853)

= 1 - (0.1853)

= 0.8146.

Therefore,The probability that among 16 randomly selected people, at least 1 believes that college is no longer a good investment is 0.815.

c).

This is a voluntary response sample, in other words, self-selected sample, which means that respondents decide whether or not to be included in the survey. This means conclusions are made about a population from a specific group of people, people who are generally more interested or passionate about the topic would participate compared to others who are not.