Question 1
“PhysicalFun†is a physical center which opens 24 hours per day.Each member of “PhysicalFun†has an access card. Members would becharged in a weekly basic (Sunday 12:00a.m. to Saturday 11: 59p.m.) according to the accumulated number of hours of facilitiesused within a week. The weekly basic charge is $150 with anadditional charge of $30 per hour. According to the company record,the number of hours a member spends in “PhysicalFun†in a week isnormally distributed with mean 15 hours and standard deviation 2.8hours.
(a) What are the average and standard deviation of weekly chargeof a member?
(b) Suppose the middle 85% of weekly charge of a member isdenoted by $(L1, L2). Find the values of L1
and L2.
(c) The senior management suggests fixing the weekly charge permember at $700. Assume the number
of hours a member spends in “PhysicalFun†would not be changeddue to the change of the weekly charge
calculation method. What proportion of members would pay moremoney than the original system?
(d) How many hours does a member spend in “PhysicalFun†in aweek so he / she would be beneficial by
the new system?
