Having measured the length of a very large number of bolts t

Having measured the length of a very large number of bolts, the average length was found to be 2.068\" with a standard deviation of 0.33\". Find the range of values that 90% of the bolts will fall within, assuming the bolt lengths are distributed normally?

Solution

Length of bolts ~ N(2.068, 0.33)

P(X<R2) - P(X<R1) = 0.9

Therefore P(X<R2) = 0.95 and P(X<R1) = 0.05

Subtraction of these two value will give 90% coverage

using R qnorm(0.95, 2.068, 0.33) = 2.610802, qnorm(0.05, 2.068, 0.33) = 1.525198

There (1.525198, 2.610802) is the range of values that 90% of the bolts will fall within this range