Respuesta :
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%=0.56
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%.
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
