A manufacturer knows that their items have a normally distributed length, with a mean of 15.2 inches, and standard deviation of 1.6 inches. If one item is chos

Question

A manufacturer knows that their items have a normally distributed length, with a mean of 15.2 inches, and standard deviation of 1.6 inches.

If one item is chosen at random, what is the probability that it is less than 12.8 inches long?

Answer 1

Get a z-score chart

https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf

 

z = (X - μ) / σ, where X = date, μ = mean, σ = standard deviation

 

z = (12.8 - 15.2) / 1.6

z = -1.500

 

0.06681 is the area for this z.

 

6.681% shall be shorter than 12.8 inches.