Find P7, which is the length separating the shortest 7% rods from the longest 93%.

Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 104.3-cm and a standard deviation of 1.6-cm.

Find P₇, which is the length separating the shortest 7% rods from the longest 93%.

P₇ =

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

HI Kaitlyn,

z=(x-µ)/σ

We know the mean and standard deviation. We need to find the z score in order to solve for "x" algebraically.

Looking through the normal distribution table (or calculator function), 0.07 corresponds to z=-2.455.

So x= zσ+μ: x= (-2.455)(1.6)+104.3=101.1cm

I hope this helps.