The time it takes Alice to walk to the bus stop from her home is Normally distri

Question

The time it takes Alice to walk to the bus stop from her home is Normally distributed with mean 12 minutes and variance 3 minutes^2. The waiting time for the bus to arrive is Normally distributed with mean 5 minutes and standard deviation 2 minutes. Her bus journey to the UBC bus loop is a Normal variable with mean 24 and standard deviation 5 minutes. The time it take Alice to walk from the bus loop to the lecture theatre to attend STAT 251 is Normally distributed with mean 18 minutes and variance 4 minutes^2. The total time taken for Alice to travel from her home to her STAT 251 lecture is Normally distributed. Please use R to find probabilities (R's pnorm0 function). Part a) What is the mean travel time (in minutes) 59 Part b) What is the standard deviation of Alice's travel time (in minutes, to 2 decimal places)? Part c) The STAT 251 class starts at 8 am sharp. Alice leaves home at 7am. What is the probability (to 2 decimal places) that Alice will not be late for her class?

Explanation / Answer

let four process are 1,2,3,4 for our journey from home to STAT 251 class

a)here mean interval time =X1+X2+X3+X4=12+5+24+18=59

b)std deviation =(S12+S22+S32+S42)1/2=(3+22+52+4)1/2=6

c)as she has to reach with in one hour i.e in 60 minutes

P(X<60)=P(Z<(60-59)/6)=P(Z<0.1667)=0.57

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