Question

suppose the width of a bus is normally distributed with a mean of 3.3 meters and standard devition .2 meters.

what is the probability that a chevy bus a width of 4 meters or more ?

a group of bus measurers observe a bus using their professional measuring estimation skills and decide that it is at least 3.8 meters before measuring it with tools. what is the probability it is 4 meters or wider?

Answer 1

This is a normal distribution question with



a) P(x > 4.0)=?
The z-score at x = 4.0 is,

z = 3.5
This implies that
P(x > 4.0) = P(z > 3.5) = 1 - 0.9997673709209645



b) The z-score at x = 3.8 is,

z = 2.5
This implies that
P(x > 3.8) = P(z > 2.5) = 1 - 0.9937903346742238

P(x > 4 | x > 3.8) = ?
P(x > 4 | x > 3.8) =
P(x > 4 | x > 3.8) =
P(x > 4 | x > 3.8) = 0.0002/0.0062
P(x > 4 | x > 3.8) = 1/31
PS: you have to refer z score table to find the final probabilities.
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