How do I fine binomial probability

Question

How do I set up and solve my problems

n=36

p=.37

q=.67

Mu=13.32

Sigma=2.90

X= the number of adults that say their favorite color is blue out of 36

 

QUESTION:

Assume 37% of adults take their favorite color is blue. In a sample of 36 randomly selected adults, find the estimated probability that more than 20 adults take their favorite color is blue.

Answer 1

Suppose a binomial experiment consists of n trials and results in x successes. If the probability of success on an individual trial is P, then the binomial probability is:

b(x; n, P) = nCx * P^x * (1 - P)^{n - x}
or
b(x; n, P) = { n! / [ x! (n - x)! ] } * P^x * (1 - P)^{n - x} where n=36 and p=.37

 

The probability that more than 20 adults take their favorite color is blue is the cumulative probability  where X >20 or Prob of X=21 + Prob of X=22 + Prob of X=23 + ... Prob of X=36

 

I will set up the first two for you so that you can do the remaining.

 

Probability of 21 or  b(21; 36, .37) =  { 36! / [ 21! (36- 21)! ] } * .37²¹ * (1 - .37)^36-21 = .0046562

 

Summing all Prob from 21 to 36 yields 0.007477928

 

Hope this helps