Questions 17-18: There are three coffee shops in a neighbourhood: TH, SB, SC. Sp

Question

Questions 17-18: There are three coffee shops in a neighbourhood: TH, SB, SC. Spending per customer per visit at TH, denoted XTH, follows the continuous distribution U[1,8]. Spending per customer per visit at SB, denoted XSB, follows U[3,16]. Spending per customer per visit at SC, denoted XSC, follows the continuous distribution N(3,3). Spending is measured in dollars in all cases.

What is the probability that a randomly selected customer at TH spends more than $7? (LO 9.4u)

ANSWER: 0.1428

Suppose that spending per visit at the three coffee shops are independent. Consider average spending per visit across the three coffee shops: Y = (XTH+XSB+XSC)/3. What is the expected value of the average spending? (LO 9.2)

anSWER. $5.67

I want to know how to get these two answers. Thanks in advance

Explanation / Answer

17) for  XTH, follows the continuous uniform distribution U[1,8] ; therefore its parameter a =1 and b=8

here probability that a randomely selected customer at TH spends more than $7 =P(X>7)=1-P(X<7)

=1-(x-a)/(b-a)=1-(7-1)/(8-1)=1-6/7=0.1428

18) here average of XTh =E(XTh) =(1+8)/2 =4.5

average of XSB =E(XSB)=(3+16)/2=9.5

and average of XSC=E(XSC)=3

therefore average spending per visit across the three coffee shops E(Y)=((E(XTH)+E(XSB)+E(XSC))/3

=(4.5+9.5+3)/3= 5.67

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