Question

The weights of certain machine components are normally distributed with a mean of 8.34 ounces and a standard deviation of 0.04 ounces Find the two weights that separate the top 4% and the bottom 4% These weights could serve as limits used to identify wich components should be rejected. Round your answer to the nearest hundredth, if necessary ANSWER Enter your answer in the boxes below. Answer ounces and ounces

Answer 1

Standardizing the value

$Z = ( X - \mu ) / \sigma$

P ( Z < ? ) = 4% = 0.04 ( Bottom 4% )

Looking for the probability 0.04 in standard normal tabel to find the critical value Z

Z = - 1.75

P ( Z > ? ) = 4% = 0.04 ( Top 4% ) = 1 - P ( Z < ? )

P ( Z > ? ) = 1 - P ( Z < ? ) = 1 - 0.04 = 0.94

Looking for the probability 0.04 in standard normal tabel to find the critical value Z

Z = 1.75

X = 8.270 ( Bottom 4% )

X = 8.410 ( Top 4 % )

The two weights that separate the top 4% and bottom 4% is 8.410 & 8.270.