Question

The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. what is the probability that a randomly selected item will weigh more than 10 ounces?

Answer 1

First we calculate z using the formula:

z = (x - μ)/σ

Where:

x = our variable, 10

μ = mean, 8

σ = standard dev, 2

Substituting known values:
z = (10 - 8)/2
z = 2/2
z = 1

Using the tables of the normal distribution to find the p-value with z = 1

p = 0.8413

Since we want "greater than 10”, we need to subtract the probability from 1 therefore

p* = 1 - 0.8413 = 0.1587