Exhibit 6-5
The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.
-Refer to Exhibit 6-5. What is the probability that a randomly selected item will weigh between 11 and 12 ounces?
A)0.4772
B)0.4332
C)0.9104
D)0.0440

Question

Quizplus · Accepted Answer

First, we need to standardize the values:
$z_{11}=\frac{11-8}{2}=1.5$
$z_{12}=\frac{12-8}{2}=2$

Then, using a standard normal distribution table, we can find the probabilities:
$P(1.5<z<2)=P(z<2)-P(z<1.5)=0.9772-0.9332=0.0440$

Therefore, the probability that a randomly selected item will weigh between 11 and 12 ounces is 0.0440, which corresponds to answer choice D.

Exhibit 6-5 The Weight of Items Produced by a Machine Is Normally