Question

A lumber cutting machine cuts lumber to a mean length of 231.0​cm, with a standard deviation of 3.4cm. The lengths are normally distributed. What is the shortest length that still places a piece of lumber in the longest 35% of​ lengths? Show your calculation and the answer rounded to the nearest hundredth of a cm.

Answer 1

Solution:

Given, the Normal distribution with,

   = 231.0

= 3.4

For longest 35% data , P(X > x) = 0.35

P(X < x) = 1 - 0.35 = 0.65

For z ,

P(Z < z) = 0.65

But from z table , P(Z < 0.385) = 0.65

Comparing we get

z = 0.385

Using z score formula ,

x = + (z * ) = 231.0 + (0.385 * 3.4) = 232.31

Answer : 232.31 cm