A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that exactly 3 support increased spending on environmental issues.
A) .0330
B) .1318
C) .7844
D) .9624

Question

Quizplus · Accepted Answer

This is a binomial distribution problem, where the number of trials (selecting 6 freshmen) is known, the probability of success (supporting increased spending on environmental issues) is given, and we need to find the probability of a specific number of successes (exactly 3). The formula for the probability of exactly x successes in n trials is:

P(x) = (nCx) * p^x * q^(n-x)

where nCx is the number of ways to choose x items out of n, p is the probability of success, q is the probability of failure (1-p), and ^(n-x) means to raise q to the power of (n-x).

Using this formula with n=6, p=0.25, and x=3:

P(3) = (6C3) * (0.25)^3 * (0.75)^3
= (20) * 0.015625 * 0.421875
= 0.1318359375

Rounding to four decimal places, we get 0.1318, which corresponds to choice B.

A Study Conducted by a Local University Found That 25