Some assembly required. A company that markets build-it-yourself furniture sells a computer desk that is advertised with the claim less than an hour to assemble. However, through postpurchase surveys the company has learned that only 25% of its customers succeeded in building the desk in under an hour; 5% said it took them over 2 hours. The company assumes that consumer assembly time follows a Normal model.

a) Find the mean and standard deviation of the assembly time model.

b) One way the company could solve this problem would be to change the advertising claim. What assembly time should the company quote in order that 60% of customers succeed in finishing the desk by then?

c) Wishing to maintain the less than an hour claim, the company hopes that revising the instructions and labeling the parts more clearly can improve the 1-hour success rate to 60%. If the standard deviation stays the same, what new lower mean time does the company need to achieve?

d) Months later, another postpurchase survey shows that new instructions and part labeling did lower the mean assembly time, but only to 55 minutes. Nonetheless, the company did achieve the 60%-in-an-hour goal, too. How was that possible?