Question

The acceptance rate for a university is 42 percent. Assuming the binomial to the normal distribution. Of the next 10 applications what is the probability that they will accept: (WHEN ROUNDING DO NOT ROUND ANY CALCULATION UNTIL THE VERY END)

a) Find the mean: μ = n ⋅ p =  round to a single decimal.

b) Calculate the standard deviation. σ = n ⋅ p ⋅ q =  . Round to 4 decimals.

c) Determine the probability that exactly four applicants will be accepted.  round to 4 decimals

d) Determine the probability that between four and six applications will be accepted.  round to 4 decimals.

e) Determine the probability that at least two of the applicants will be accepted. (You may use the complement rule here).  round to 4 decimals.

f) What is the probability for the university to accept none or more than 7 applications?  Round to 4 decimals. Would it be unusual for the university to accept no or more than 7 applicants?  Yes/No.

Answer 1

Since in the question it is said that binomial to normal is assumed, so here I use normal probability.

But in fact for normal approximation validity 2 conditions must be satisfied,

n*p should be greater than 5 and n*(1-p) should be greater than 5, bt here it will not satisfied.

And also there is a mistake in the question that the standard deviation is not n*p*q it is square root of npq.

I think binomial distribution is useful in this question.if any doubt please mension in the comment section.