lthough cities encourage carpooling to reduce traffic congestion, most vehicles
ID: 3124983 • Letter: L
Question
lthough cities encourage carpooling to reduce traffic congestion, most vehicles carry only one person. For example, 68% of vehicles on the roads are occupied by just the driver. (Round your answers to four decimal places.)
(a) If you choose 10 vehicles at random, what is the probability that more than half (that is, 6 or more) carry just one person?
(b) If you choose 92 vehicles at random, what is the probability that more than half (that is, 47 or more) carry just one person? (Use the normal approximation.)
Explanation / Answer
Probability that a vehicle on the road is occupied by just the driver is .68
a. P( that more than half carry just one person) = P(X=6)+P(X=7)+P(X=8)+P(X=9+P(X=10) = 10C6*(0.68)^6*(0.32)^4 + 10C7*(0.68)^7*(0.32)^3+10C8*(0.68)^8*(0.32)^2+10C9*(0.68)^9*(0.32)^1+10C10*(0.68)^10*(0.32)^0
= 0.2177+0.2643+0.2106+0.09947+0.021139 = 0.81329
b. Mean value is np = 92*0.68 = 62.56 and variance is npq = 92*0.68*0.32 = 20.02
P(X>47) = P(Z>((47-62.56)/4.474)) = 0.9997
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