Question

Hi, so I am confused on this problem. When I first look at this it seems the P(0) and P(1) make sense but P(2) kind of seems high compared to P(3) Is anyone able to help me explain what or what doesn't make sense?

Do these probabilities make sense?

Use the values you found for P(3), the mean, and standard deviation to determine if P(0), P(1), and P(2) are reasonable and make sense.

P(3)= 0.01458

Mean: 0.6

Standard Deviation: 0.73

P(0)=0.531

P(1)=0.354

P(2)= 0.0984

You’re a researcher looking at whether or not applicants are accepted to a prestigious law internship. A group of 6 friends apply. Only 10% of applicants receive a call to a first interview.

Answer 1

This is a problem of binomial distribution

Here, n= 6 and p= probability of success= 0.1

So mean = n*p= 0.6 and

Standard deviation=√n*p*(1-p)= 0.73

If X follow binomial (n,p) distribution then

P(X=x)= nCx*p^x*(1-p)^(n-x)

So, in this way we get P(2) = 0.0984, P(3) = 0.01458 and so on

Therefore the probability of the number of applicants to be accepted to a prestigious law internship is decreasing when the number is getting higher

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