Question

2017 poll found that 56​% of college students were very confident that their major will lead to a good job. If 20 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: 0.1318

Step-by-step explanation:

Given : The proportion of college students were very confident that their major will lead to a good job : p= 0.56

Let x be the binomial variable (for success) that represents the number of college students were very confident that their major will lead to a good job.

with parameter p = 0.56  n= 20

Using binomial , we have

$P(x)=^nC_xp^x(1-p)^{n-x}$

Required probability :-

$P(x=13)=^{20}C_{13}(0.56)^{13}(1-0.56)^{20-13}\\\\=\dfrac{20!}{13!7!}(0.56)^{13}(0.44)^{7}\\\\=0.131833824312\approx0.1318$

Hence, the probability that 13 of them were very confident their major would lead to a good​ job =0.1318