Question

Number of customers coming to a massage parlor follows a Poisson distribution with 1 = 4 customers per hour. Let the amount spent (in dollars) by a customer be distributed as N(80, 900). a.(4 points) If the shop opens at 9 am, what is the probability that the first customer arrives between 9:30 am and 10 am? b. (8 points) What is the probability that the parlor makes a revenue of more than $100 within an hour of its opening? Assume that the parlor can serve upto a maximum 3 customers per hour.

Answer 1

the no. 01 " Probability solution - Let X be number of customers thout Follows Poisson distribution with 8=4. Xn Pois (4) Y; be the amount spent by the ith customero distroibuted as AM120,000) dey NC80, olc 9009 ay a Ff 2 = 4 pero hours then a = 4X42 pes (half of an Let wu be the random variable that de notes customers coming in every 30 mins. then wen pois (2). that the 1st con customers annives between 9:30 and 10:30 = PC U=1) é 24 (2) =é 2 I = 0027067 ~ 0.271 that the baslono con sepre z wstomers' pero houp. sefer Probability that the parlon makes a pevenue of more thon $100 within an hour = 9x=1] [Y) 100X=1] 7 Ppx=2] P[izri7100) X = 2] 7 P[X=3] p[;ZY: %100X = 3] ANS by Assuming opport a maximum of

Mi is 2 = Tolf oppler 3 53684):73} PlMix 100 W/78177112 'Indepen. Mittene of x tie 14 PCZY > 100172 Pliyi 3 100 2B) Dette TY, NCP9,900) N(80 +80, 9200 +900) Eyim N(80780480,9072980 tamo a tepay any 0.01849825 + 0-135001 + 0.1946798 an Eli 1=1 in ia 11 = 0.3481471 zi 0.248 ANS