Question

a. A 2017 poll found that 56​% of college students were very confident that their major will lead to a good job. If 15 college students are chosen at​ random, what's the probability that 13 of them were very confident their major would lead to a good​ job? Let a success be a college student being very confident their major would lead to a good job.

Answer 1

Answer:

0.01083 or 1.083%

Step-by-step explanation:

This problem can be modeled as a binomial probability model with probability of success p = 0.56.

The probability of x=13 successes (a college student being very confident their major would lead to a good job) in a number of trials of n=15 is:

$P(X=x) = \frac{n!}{(n-x)!x!} *p^x*(1-p)^{n-x}\\P(X=13) = \frac{15!}{(15-13)!13!} *0.56^{13}*(1-0.56)^{15-13}\\P(X=13) = 0.01083=1.083\%$

The probability is 0.01083 or 1.083%.