Two alirplanes are flying Iin the same direction in adjecent paralilel corridors

Question

Two alirplanes are flying Iin the same direction in adjecent paralilel corridors. At time t-0, the first airplane is 10 km ahead of the second one. Suppose the speed of the first pliane with mean 530 and standard deviation 9 and the second plane's speed is also normally distributed with mean and standard deviation 510 and 9, (a) What is the probability that after 2 hr of flying, the second plane has not caught up to the first plane? (Round your answer to four decimal places) (b) Determine the probability that the planes are separated by at most 10 km ater 2 hr (Round your answer to four decimal places)

Explanation / Answer

X1 = 10 + v1 *2

where v1 ~ N(530,9^2)

X1 ~ N(1070 , 9^2)

X2 = v2 * 2

v2~ N(510,9^2)

X2 ~ N(1020 , 9^2)

X1 - X2 ~ N(50 , 9^2 + 9^2)

~N(50, 2 *9^2)

a) P(X2 < X1)

= P( X1 - X2 > 0)

= P(Z > (0 - 50)/(9* sqrt(2))

=P(Z> -3.928371)

= 1

b) P(|x1- X2| < 10)

= P(-10 <X1 -X2 < 10)

= P((-10 - 50)/(9* sqrt(2)) < Z< (10 - 50)/(9* sqrt(2)))

= P( -4.714045 <Z< -3.14269 )

= 0.0008

Please rate

b)

=0.999957

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