Question

The time it takes for an emergency medical squad to arrive at a building in NYC is distributed as a normal distribution with the mean 8 minutes and standard deviation of 2 minutes.

(a) After _____ minutes, 90% of the squad trips will arrive at their destination.

(b) What is the probability that a squad arrives within 10 minutes?

(c) Find the probability that the squad will arrive in between 6 to 11 minutes.

(d) Suppose that two emergency medical squads leave for their respective destinations around the same time and that the two squads’ travels are independent of each other. Find the expected total travel time for the two squads. Find the standard deviation of the total travel time of two squads.

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	8
std deviation   =σ=	2.000

for 90th percentile critical value of z=		1.28
therefore corresponding value=mean+z*std deviation=8+1.28*2 =			10.56 minutes

b)

probability =P(X<10)=(Z<(10-8)/2)=P(Z<1)=0.8413

c)

probability =P(6<X<11)=P((6-8)/2)<Z<(11-8)/2)=P(-1<Z<1.5)=0.9332-0.1587=0.7745

d)

expected total travel time =E(x1+x2) =E(x1)+E(X2)=8+8 =16 minutes

standard deviation of the total travel time =sqrt(Var(x1)+Var(x2))=sqrt(2^2+2^2)=2.8284