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irina1246 [14]
3 years ago
9

A 2017 poll found that 51​% of college students were very confident that their major will lead to a good job. If 15 college stud

ents are chosen at​ random, what's the probability that 11 of them are NOT confident that their major would lead to a good​ job? Let a success be a college student not being confident their major would lead to a good job.
Mathematics
1 answer:
murzikaleks [220]3 years ago
3 0

Answer:

3.61%

Step-by-step explanation:

This situation can be modeled with the Binomial Distribution which computes the likelihood of an event “success” that occurs exactly k times out of n, and is given by

\large P(k;n)=\binom{n}{k}p^kq^{n-k}

where  

\large \binom{n}{k}= combination of n elements taken k at a time.

<em>p = probability that the event (“success”) occurs once </em>

<em>q = 1-p </em>

In this case, we define “success” as a college student not being confident that their major would lead to a good job.

Then  

p = 49% = 0.49

q = 51% = 0.51

“If 15 college students are chosen at​ random, what's the probability that 11 of them are NOT confident that their major would lead to a good​ job?”

Here we are looking for P(11;15)

\large P(11;15)=\binom{15}{11}0.49^{11}0.51^{(15-11)}=0.03611=3.61\%

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