Question

Suppose that 9% of people in Canada say that red is their favourite colour. Consider the sampling distribution of ˆp with n = 75. (The population of Canada is 38250000 people)

Given that P[ˆp > A] = 0.3771, find A.

Given that P[ˆp < B] = 0.94, find B

Answer 1

To find A and B, we use the standard normal distribution and the z-score formula.

Step-by-step explanation:

To find A, we need to find the value of ˆp that has a cumulative probability of 0.3771. Since we know that the sampling distribution of ˆp is normally distributed with a mean of p and a standard deviation of √(p(1-p)/n), we can use a standard normal distribution to find the z-score corresponding to a cumulative probability of 0.3771. We can then use the z-score formula to find A. Similarly, to find B, we need to find the z-score corresponding to a cumulative probability of 0.94 and use the z-score formula.