7. You and a friend are trying to decide on where to go for an evening out. Your

Question

7. You and a friend are trying to decide on where to go for an evening out. Your friend does not get out much, so you want to make sure you have a good time. She gets very uncomfortable in crowded places, so you must choose the locale for the evening carefully. Luckily, you routinely keep data on the capacity of the restaurants that you visit, and have the tables below readily available. Use this information to pick where you and your friend will go out Paddy's Pub The Gairison ac 13% 24% 41% 53% 100% Probabil 0.075 0.215 0.35 0.265 0.095 ac 31% 42% 56% 6490 73% Probab 0.15 0.25 0.15 0.25 0.2 A) What is the expected value and standard deviation of capacity for Paddy's Pub? B) What is the expected value and standard deviation of capacity for The Garrison? C) Which restaurant will you and your friend go to tonight? Why?

Explanation / Answer

7.

A.
paddy's pub
expected value = x*p(x)
standard deviation = sqrt(v(x))
variance v(x) = sum of x^2*p(x) - (sum of x*p(x))^2)
expected value = (13*0.075+24*0.215+41*0.35+53*0.265+100*0.095) = 44.03
variance v(x) = (13^2*0.075+24^2*0.215+41^2*0.35+53^2*0.265+100^2*0.095) -(44.03)^2 = 480.6091
standard deviation = sqrt(v(x)) = sqrt(480.6091) = 21.9227

B.
The garrison
expected value = x*p(x)
standard deviation = sqrt(v(x))
variance v(x) = sum of x^2*p(x) - (sum of x*p(x))^2)

expected value = (31*0.15+42*0.25+56*0.15+64*0.25+73*0.2) =54.15
variance v(x) = (31^2*0.15+42^2*0.25+56^2*0.15+64^2*0.25+73^2*0.2) =213.1275
standard deviation = sqrt(v(x)) = 14.5988

C.
paddy pub is going tonight because expected value and standard deviation are both more than the garrison so that he will go and opt for paddy pub

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