Finding the probability

Question

For my stats class, we have to do probability. We had to create a survey. So I surveyed 32 people asking "Do you like chocolate?" I got 23 yes, and 9 no's. A success is people saying yes. So the questions are : 5. What is p, the probability of a success according to your answers to 2 and 3?

p =

6. Suppose we can treat your survey as a binomial experiement, what is the probability that you will get at least 10 successes out of 30 people?

7. Suppose we can treat your survey as a binomial experiment, use your p to construct the following probability distribution if n = 3.

x 0 1 2 3
P(x)

Answer 1

p=9/23 = 0.39

p(X >=10| 30, 0.39) = 1- p(X<=9)

 = 1- {p(X=0) + p(X=1) + p(X=2) +... + p(X=9)} ..... Equation 1

To compute any of the probability inside Equation 1, use the Binomial probability formula

  p(X=x |n, p) = (n!/x!(n-x)!) * p^x * (1-p)^(n-x)