Probability question 2?

2) A market researcher typically obtains answers from 1 shopper in 4. If 15 shoppers are interviewed:





a) What is the probability that nobody answers?


b) What is the probability that exactly 5 people answer?


c) What is the probability that less than 10 answer? (Use tables)


d) What is the variance of the number of answers?





Please explain how i would work these out and answers, i have an exam and i don't know how to work these out. Thanks in advance.

Probability question 2?
a) 3/4 dont answer. if 15 people don't answer


p(no one answers) = 3/4 ^15





b) p(5 people answer) - use binomial distribution.


15C5 * 1/4 ^5 * 3/4 ^ 10





c) p(%26lt;10 answer) = 1 - p(%26gt;=10 answer) =


1 - ( (15C10 * 1/4^10 * 3/4^5) + (15C11 * 1/4^11 * 3/4^4) +


(15C12 * 1/4^12 * 3/4^3) + (15C13 * 1/4^13 * 3/4^2) +


(15C14 * 1/4^14 * 3/4^1) + (15C15 * 1/4^15 * 3/4^0) )





d) not sure

phlox