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

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