Question

A survey found that 8 out of 10 parents approved of the new principals performance.If 14 parents names are chosen with replacement what is the probability they all approve of the principals performance

Answer 1

The probability is 0.044

Explanation:

Let p be the probability that the new principal’s performance is approved.

This is obtainable from the survey and it is 8/10 = 0.8

Let q be the probability that the new principal’s performance is disproved.

That will be;

1 - q = 1- 0.8 = 0.2

To calculate the probability that 14 parents names are chosen at random and they all

approve of the principal’s performance, we use the Bernoulli approximation of the binomial theorem.

That will be;

14C14 * p^14 * q^0

= 1 * 0.8^14 * 0.2^0

= 0.043980465111 which is approximately 0.044