A company that makes products designed for people who have long commutes is thinking about expanding into Nova Scotia. For their business purposes, the company defines a long commute as one that is 10 km or more. The company will only expand into Nova Scotia if the proportion of commuters who have a long commute is more than 0.46; they hire market researchers to conduct a survey to gather the data.

Unknown to the company and market researchers, the true proportion of Nova Scotian commuters who have a long commute is 0.422 . If the market researchers take a survey of 521 Nova Scotians commuters, what is the probability that more than 46% of their sample will have a long commute? [You will answer this question in parts.]

1. What is the mean of the sampling distribution of , the sample proportion of commuters with a long commute?

2. What is the standard deviation of the sampling distribution of , the sample proportion of commuters with a long commute? (Round your answer to 3 decimal places.)

3. What is the z-score for determining if more than % of the commuters in the sample have (Use your values from parts 1 and 2. Round your answer to 2 decimal places.)

4. What is the probability that more than 46% of their sample will have a long commute?

A)1.9164

B) 0.0418

C) 0.0836

D) 0.9582