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 no more than 3.5 ounces?
A).8413
B).9772
C).1587
D).0228

Question

Quizplus · Accepted Answer

To solve this problem, we need to standardize the weight using z-score formula:
$z=\frac{x-\mu}{\sigma}$
where:
$\mu=4$ (mean)
$\sigma=\sqrt{0.25}=0.5$ (standard deviation)
$x=3.5$ (weight we want to find the probability for)

$z=\frac{3.5-4}{0.5}=-1$
Now we can find the probability of a standard normal variable being less than or equal to -1 using normal distribution table, which gives us:
$P(Z\leq -1)=0.1587$
Therefore, the probability that a randomly selected unit from the batch weighs no more than 3.5 ounces is 0.1587 or 15.87%.
The correct answer is (C).

The Weight of a Product Is Normally Distributed with a Mean