Question: 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:

Phase                Mean            SD

Unpacking           3.5              0.7

Assembly           21.8              2.4

Tuning              12.3              2.7

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.