The weight of a product is normally distributed with a mean 5 ounces.A randomly selected unit of this product weighs 7.1 ounces.The probability of a unit weighing more than 7.1 ounces is .0014.The production supervisor has lost files containing various pieces of information regarding this process,including the standard deviation.Determine the value of the standard deviation for this process.
A)1.67
B)0.70
C)2.10
D)0.50

Question

Quizplus · Accepted Answer

The z-score corresponding to a probability of 0.0014 in the upper tail of a standard normal distribution is approximately 3.00. Using the z-score formula $ z = \frac{X - \mu}{\sigma} $, where $ X = 7.1 $, $ \mu = 5 $, and $ z = 3.00 $, we solve for $ \sigma $: $ 3.00 = \frac{7.1 - 5}{\sigma} $. This gives $ \sigma = \frac{2.1}{3.00} = 0.70 $.

The Weight of a Product Is Normally Distributed with a Mean