how to solve this question

Question

Over a long period of time in a large multinational corporation, 10% of all sales trainees are rated as outstanding, 75% are rated as execellent/good, 10% are rated as satisfactory, and 5% are considered unsatisfactory. Find the following probabilities for sample of 10 trainees selected at random.

A- Two are rated as outstanding

B- Two or more are rated as outstanding

C- Eight of the 10 are rated either outstanding or execellent/good

D- None of the trainees is rated as unsatisfactory

Answer 1

I think these questions are supposed to be answered using the binomial distribution function.  I will give you some suggestions, but I will not solve the problem for you entirely.

 

The probability of outstanding is 10%; that means probability of "not outstanding" is 90%.  The answer to "A" then is the third term in the binomial density with p=.1 and q=.9.

 

Two or more outstanding means 0 or 1 not outstanding.  For "B" You need the last 2 terms in the same binomial density as in "A" and you subtract the sum of those 2 terms from 1.

 

For "C" your binomial changes: p=.85 and q=.15.  Her you want the sum of the 1st two terms subtracted from 1 

 

For "D" your binomial p=.05 and q=.95 and you want only the first term.