Question

1. Laura crafts clay coffee mugs to sell in local gift shops. The total time it takes her to make a single mug is normally distributed with a mean of 70 minutes and a standard deviation of 7 minutes

a) What percent of mugs take longer than 80 minutes to make?

b) Bean There, Done That coffee shop has made an order that will require a large amount of mugs to be made. Laura calculates that if more mugs can be made in less than 80 minutes apiece, the order can be filled on time. What standard deviation would need to be achieved to ensure that 95% of all mugs are finished in less than 80 minutes?

c) Explain what achieving a smaller standard deviation means in the context of this problem.

d) On Saturdays, Laura takes “while you wait” orders for mugs, which allow customers to place an order and come back to pick it up when it is finished. The sign for the service tells customers to expect to wait 60-75 minutes before pickup. What proportion of the time is the sign accurate?

Answer 1