Question

Eighty percent of the students applying to a university are accepted. Using the binomial probability tables or Excel, what is the probability that among the next 20 applicants:

1. Exactly 10 will be accepted? Why is this number so low? (#4 might help)

2. At least 14 will be accepted? (14 or more will be accepted)

3. Exactly 5 will be rejected?

4. Determine the expected number of acceptances.

5. Compute the standard deviation.

I do not know how to use the binomial tables and the standard deviation formula.

Answer 1

Please don't hesitate to give a "thumbs up" for the answer in case you're satisfied with it.

We have been given params of normal distribution, as below:

p= 0.80

n = 20

1. Exactly 10 will be accepted?

= 20C10*(.8^10)*(1-.8)^10 = 0.0020

This number is low because the expected number of acceptance is much higher, which is actually n*p = .8*20 = 16, a number much higher than 10

2. At least 14 will be accepted ?

P(X>=14)

= 20C14*(.8^14)*(1-.8)^6+...+ 20C20*(.8^20)*(1-.8)^0

= 0.9133

3. Exactly 5 will be rejected

P(X=5)

= 20C5*(.8^5)*(1-.8)^15

=

1.66473E-07

4.

Expected number of acceptances = n*p = .8*20 = 16

5.

Standard deviations = sqrt(n*p*(1-p)) = sqrt(20*.8*.2)

= 1.789