Question 1 PhysicalFun is a physical center which opens 24 hours per d...

Question 1 â€œPhysicalFunâ€ is a physical center which opens 24 hours per day. Each member of â€œPhysicalFunâ€...

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Question 1
â€œPhysicalFunâ€ is a physical center which opens 24 hours per day.Each member of â€œPhysicalFunâ€ 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 â€œPhysicalFunâ€ in a week isnormally distributed with mean 15 hours and standard deviation 2.8hours.
(a) What are the average and standard deviation of weekly charge ofa member?
(b) Suppose the middle 85% of weekly charge of a member is denotedby $(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 â€œPhysicalFunâ€ would not be changed dueto the change of the weekly charge
calculation method. What proportion of members would pay more moneythan the original system?
(d) How many hours does a member spend in â€œPhysicalFunâ€ in a weekso he / she would be beneficial by
the new system?

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AnswerGiven thatPhysicalFun is a physical center that opens 24 hours per dayEach member of PhysicalFun has an access cardMembers would be charged on a weekly basis Sunday 1200am toSaturday 11 59 pm according to the accumulated number of hoursof facilities used within a weekThe weekly basic charge is 150 with an additional charge of 30per hourAccording to the company record the number of hours a memberspends in PhysicalFun in a week is normally distributed See Answer

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Question 1 â€œPhysicalFunâ€ is a physical center which opens 24 hours per day. Each member of â€œPhysicalFunâ€...