18% of her clients schedule 30-minute sessions, 39% schedule 45-minute sessions, 32% schedule 60-minute sessions, and...

18% of her clients schedule 30-minute sessions, 39% schedule 45-minute sessions, 32% schedule 60-minute sessions, and 11% schedule 90-minute sessions.

(a) If the random variable X represents the time a client schedules for his/her session, find the probability distribution of X.

(b) Suppose that the massage therapist charges $50 per hour, and that she uses $12 in supplies per session. Find the expectation of her profit per session.

Expert Solution

a) X represents the time a client schedules for his/her session
From the given data we get the Probability Distribution of X as below :

b)   Charge = $50 per hour
   Expense = $12 per session
   Thus, Expected profit per session = P(X) * [X * 50/60 - 12]
   Thus, we have

Net Expected Profit = 2.34+9.945+12.16+6.93
= $ 31.375

orchestra answered 1 year ago

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