Annmarie is trying to decide whether to take the train or the bus into the city.

Question

Annmarie is trying to decide whether to take the train or the bus into the city. The train takes longer but is more predictable than the bus because there are no traffic delays. Train times are normally distributed with a mean of 60 minutes and standard deviation of 2 minutes, while bus times are also normally distributed with a mean of 50 minutes and standard deviation of 8 minutes. The bus and train times are independent of each other. Find the probability that the train is faster on any given day.

The correct answer is P(Z < -1.21) = .1131. I just need to know how they came to that answer.

Explanation / Answer

here let bus is X ; and train is Y

hence std error of differnce =(22+82)1/2 =8.246

also expected difference =E(X-Y)= 50-60 =-10

for train to be faster X-Y should be >0 as timing taken by bus should be longer then train

hence P(X-Y>0) =P(Z>(0-(-10)/8.246)=1-P(Z<1.2127)=1-0.8874 =0.1126

for above answer you can do (Y-X<0) and you will get above result

please revert for further clearificcation

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