stats a manaufactur

Question

A manufacturer knows that their items have a normally distributed length, with a mean of 18.2 inches, and standard deviation of 3.3 inches.

If one item is chosen at random, what is the probability that it is less than 20 inches long?

Answer 1

This would be a problem using the Z-score for 20 inches using the information above.

 

P(20 Inches) = Z-score = (x - µ)/σ    or (x - mean)/standard deviation.

 

This works out to Z- score = (20-18.2)/3.3 = 0.5454.

 

From a Z-score table (like this one): 

 

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

 

you get approx .7073 (iterating between the two values on the table).  Since you are looking for the probability of less than 20 inches long, you use all of this value so:

 

P(20 inches) = 70.73%

 

Jeff N.