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.

Given : 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.

To find : What's the probability that 13 of them were very confident their major would lead to a good job?

Solution :

Applying Binomial distribution,

[tex]P(x)=^nC_x p^x q^{n-x}[/tex]

Here, p is the success p=56%=0.56

q is the failure [tex]q= 1-p=1-0.56=0.44[/tex]

n is the number of selection n=15

The probability that 13 of them were very confident their major would lead to a good job i.e. x=13

Substitute the values,

[tex]P(13)=^{15}C_{13} (0.56)^{13} (0.44)^{15-13}[/tex]

[tex]P(13)=\frac{15!}{13!2!}\times (0.56)^{13}\times (0.44)^{2}[/tex]

[tex]P(13)=\frac{15\times 14}{2\times 1}\times (0.56)^{13}\times (0.44)^{2}[/tex]

[tex]P(13)=105\times (0.56)^{13}\times (0.44)^{2}[/tex]

[tex]P(13)=0.0108[/tex]

The probability that 13 of them were very confident their major would lead to a good job is 1.08%.

maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-03-16T05:38:19+01:00

By applying binomial distribution we got that probability that 13 of them were very confident their major would lead to a good job is 0.0108

What is probability ?

Probability is chances of occurring of an event.

Given that 56% of college students were very confident that their major will lead to a good job.

we are selecting 15 college students at random ,and we have to find probability that 13 of them were very confident their major would lead to a good job.

We can find this using Binomial distribution

[tex]P(x)={ }^{n} C_{x} p^{x} q^{n-x}[/tex]

Here, p is the success

q is the failure

n is the number of selection

Let a success be a college student being very confident their major would lead to a good job.

Hence P =56%=0.56

q=1-p=1-0.56=0.44

n=15

probability that 13 of them were very confident their major would lead to a good job can be calculated as

[tex]P(13)={ }^{15} C_{13}(0.56)^{13}(0.44)^{15-13} \\[/tex]

[tex]&P(13)=\frac{15 \times 14}{2 \times 1} \times(0.56)^{13} \times(0.44)^{2} \\[/tex]

[tex]&P(13)=105 \times(0.56)^{13} \times(0.44)^{2} \\\\&P(13)=0.0108[/tex]

By applying binomial distribution we got that probability that 13 of them were very confident their major would lead to a good job is 0.0108

To learn more about probability visit : brainly.com/question/24756209