Question

The weight of a product is normally distributed with a mean 10 ounces. A randomly selected unit of this product weighs 13 ounces. The probability of a unit weighing more than 13 ounces is 0.0014. The production supervisor has lost files containing various pieces of information regarding this process including the standard deviation. Determine the value of standard deviation for this process.

Answer 1

Given that the weight of product is normally distributed with mean = 10 ounces.

randomly selected one product weights 13 ounces.

P( X > 13 ) = 0.0014

So P( X < = 13) = 1 - 0.0014 = 0.9984

Using Z table we get ,

P( Z < = 2.98) = 0.9986 .........................see row 2.9 and column 0.08 in Z table

we get ,

So Z score is given by

So ,

Standard deviation is 1.0067