Probability and statistics

Question

A survey found that 37% of people earning between $30,000 and $75,000 said that they were very happy. If 5 people are selected at randorn, find the probability that at most 1 person who earns between $30,000 and $75,000 would consider themselves very happy. Round your answer to four decimal places.

The probability that at most 1 out of the 5 people who earn between $30,000 and $75,000 would consider themselves very happy is approximately?

Answer 1

X = number of people earning between $30,000 and $75,000 who said that they were very happy.

X ~ Binomial(n=5, p = .37)

P(at most 1) = P(X <=1)

= P(X=0) + P(X=1) = 5C0 * p^0*(1-p)^5 + 5C1 * p^1*(1-p)^4

= 5C0 * p^0*(1-p)^5 + 5C1 * p^1*(1-p)^4

= 1 * .37^0*(.63)^5 + 5* .37^1*.37^4

= .39067