Bike sale. The bicycle shop in Exercise 42 will be offering 2 specially priced children’s models at a sidewalk sale. The basic model will sell for $120 and the deluxe model for $150. Past experience indicates that sales of the basic model will have a mean of 5.4 bikes with a standard deviation of 1.2, and sales of the deluxe model will have a mean of 3.2 bikes with a standard deviation of 0.8 bikes. The cost of setting up for the sidewalk sale is $200.

a) Define random variables and use them to express the bicycle shop’s net income.

b) What’s the mean of the net income?

c) What’s the standard deviation of the net income?

d) Do you need to make any assumptions in calculating the mean? How about the standard deviation?

Exercise 42

Bikes. Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the shop manager makes the following assumptions about how long this may take:

• The times for each setup phase are independent.

• The times for each phase follow a Normal model.

• The means and standard deviations of the times (in minutes) are as shown:

a) What are the mean and standard deviation for the total bicycle setup time?

b) A customer decides to buy a bike like one of the display models but wants a different color. The shop has one, still in the box. The manager says they can have it ready in half an hour. Do you think the bike will be set up and ready to go as promised? Explain.