On a dry survace, the braking distance (in meters) of a Ford Expedition can be a

Question

On a dry survace, the braking distance (in meters) of a Ford Expedition can be approximated by a normal distribution, with mean 52 and standard deviation 2.5 m.

a) find the probability that a randomly selcted Expedition has braking distance between 50 and 55m.

b) what percentage of Expeditions, selcted randomly, have braking distances more than 50m?

c) What braking distance of a Ford Epedition represents the 95th percentile?

d) what braking distance of a Ford Epedition represents the third quartile?

e) what is the shortest braking distance of a ford expedition that can be in the top 10% of braking distances?

f) what is the longest braking distance of a Ford Expedition that can be in the bottom 5% of braking distances?

g) If 20 Ford Expeditions are randomly selected, what is the probability that the mean braking distance is less than 53m?

Explanation / Answer

mean = 52 , s = 2.5

a)
P(50 < x < 55)

z = ( x - mean) / s
= (50 - 52) / 2.5
= -0.8

z = ( x - mean) / s
= (55 - 52) / 2.5
= 1.2
P(50 < X < 55 ) = P(-0.8 < z < 1.2) = 0.6731

b)
P( x > 50)

z = ( x - mean) / s
= (50 - 52) / 2.5
= -0.8
P(X > 50 ) = P( Z > -0.8) = 0.7881

c)
z value at 95% = 1.96

x = mean + z * s
= 52 + 1.96* 2.5
= 56.9

e)
z value at 10% = 1.2815

x= mean + z * s
= 52 + 1.2815 * 2.5
= 55.203
f)
z value at 5% = -1.6448

x= mean - z * s
= 52 - 1.6448 * 2.5
= 47.888

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