You are the manager of a restaurant that delivers pizza in a given neighborhood. The average number of delivery requests you get per day is 42 and the standard deviation of number of orders is 12. You take a sample of 25 days.

a. What is the probability of getting a sample average number of orders that is bigger than 45?

b. Do you need to make any any assumption regarding the population distribution to answer part (a)? Why or why not? Explain carefully.

c. For your sample of 25 days, the sample average number of orders lies between which two values with 85% chance?

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A report on Men in Business claims that 53% of the self-emplyed men started their own business to have more flexible working hours. Suppose we take a sample of 2500 self-employed men in Canada.

a. What is the probability that 55% or more of self-emplyed men in this sample started their own business to have more flexible working hours?

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b. Now suppose a random sample of 250 self-employed men is taken. What is the probability that 55% or more of self-emplyed men in this sample started their own business to have more flexible working hours?

of 3 c. How and why does your answer in part (b) differ from that in part (a). Explain in detail. of 3