Refer to the heights of pillars in the example on page 15. The variation in the

Question

Refer to the heights of pillars in the example on page 15. The variation in the population of heights of pillars can be modeled as a normal distribution with mean 306.6 nm and standard deviation 37.0 nm.

A) For a pillar selected at random, what is the probability that its height is greater than 350 nm.

B) According to the normal model, what proportion of all existing pillars has heights greater than 350 nm? Explain your answer

C) What proportions of the pillars has heights between 270 nm and 350 nm?

Explanation / Answer

mean = m = 306.6 mm

standard deviation = s = 37 mm

z = (x - m)/s

Now,

P(x>350) = P(z > 1.17)

P(x>350) = 0.8790

This is normal distribution in that,

height of pillar greater than 350mm is having probability of 0.8790

3.

P(270<x<350) = P( - 0.99 < z < 1.18)

P(270<x<350) = P(z<1.18) - P(z<-0.99)

P(270<x<350) = 0.8790 - 0.1611

P(270<x<350) = 0.7179

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