Question

In a large population, about 45% of people prefer tea over coffee. A researcher takes a random sample of 13 people and surveys whether they prefer tea over coffee.

Use the binomial distribution to compute the probability that exactly 6 of the people in the sample prefer tea over coffee.

Identify the following information required to find the probability of people who prefer tea over coffee.

Provide your answer below:

n =  trials

x =  successes

p =   probability of those who prefer tea

Answer 1

solution:

Solution

Given that ,

p=0.45

n=13

q = 1 - p =1-0.45 =0.55

Using binomial probability formula ,

P(X = x) = (n C x) * px * (1 - p)n - x

P(X = 6) = (13 C 6) * 0.45⁶ * (0.55)^13-6

⁼ (13 C 6) * 0.45⁶ * (0.55)⁷

= 0.2169

Probability = 0.06