Question

Let's assume our class is truly representative of the population at large. (a) Calculate the probability of having three right handed people in a sample of 10. Do this using R. (b) repeat, but this time calculate the probability of 3 or less right handed people in a sample of 10.n=17 right handed= 15 left handed=2

Answer 1

0.1171875;

0.171875

Explanation:

It is either a person is right handed or left handed

P(right handed) = 1/2

Probability of having 3 right handed people in a sample of 10 ;

P(x =x) = nCx * p^x * (1 - p)^(n - x)

P(x = 3) = 10C3 * 0.5^3 * 0.5^7

P(x = 3) = 120 * 0.125 * 0.0078125

P(x = 3) = 0.1171875

Using R ;

P(x ≤ 3)

We can obtain these from R using ;

pbinom( r, n, p)

pbinom(3, 10, 0.5) = 0.171875