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.
Accepted Solution
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Answer:The probability that 13 of them were very confident their major would lead to a good job is 1.08%.Step-by-step explanation: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%=0.56q is the failure [tex]q= 1-p=1-0.56=0.44[/tex]n is the number of selection n=15The probability that 13 of them were very confident their major would lead to a good job i.e. x=13Substitute 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%.