The weight of a product is normally distributed with a mean of four ounces and a variance of .25 "squared ounces." What is the probability that a randomly selected unit from a recently manufactured batch weighs more than 5 ounces?
A).0228
B).9772
C)0.000
D)1.00

Question

Quizplus · Accepted Answer

To solve the problem, we need to standardize the variable x (the weight of the product) using the formula:

z = (x - μ) / σ

where μ is the mean and σ is the standard deviation (not the variance).
In this case, μ = 4 ounces and σ² = 0.25 squared ounces, so σ = 0.5 ounces.
Therefore,

z = (x - 4) / 0.5

Now we want to find the probability that x > 5 ounces, which is equivalent to finding the probability that z > (5 - 4) / 0.5 = 2.

Using a standard normal distribution table or calculator, we find that P(z > 2) = 0.0228. Therefore, the answer is A) 0.0228.

The Weight of a Product Is Normally Distributed with a Mean