The weights of extra-large eggs have a Normal distribution with a mean of 1 ounces and a standard deviation of 0.1 ounces.What is the probability that a carton of a dozen eggs weighs more than 13 ounces?
A)0.0000
B)0.0019
C)0.1814
D)0.2033

Question

Quizplus · Accepted Answer

Let's use the formula for the sample mean of a sample of size n from a normal population:

$\bar{X} = \mu$

$\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}$

where $\mu$ is the population mean, $\sigma$ is the population standard deviation, $\bar{X}$ is the sample mean, and $\sigma_{\bar{X}}$ is the standard deviation of the sample mean.

For a carton of 12 eggs, the sample mean is:

$\bar{X} = 1$

and the standard deviation is:

$\sigma_{\bar{X}} = \frac{0.1}{\sqrt{12}} \approx 0.029$

To find the probability that the carton weighs more than 13 ounces, we need to find the z-score:

$z = \frac{13 - \bar{X}}{\sigma_{\bar{X}}} = \frac{13 - 1}{0.029} \approx 413.79$

Using a standard normal distribution table, we find that the probability of a z-score greater than 413.79 is approximately 0. Therefore, the probability of a carton of a dozen eggs weighing more than 13 ounces is very close to 0.

The only choice that is close to 0 is B, so B is the answer.

The Weights of Extra-Large Eggs Have a Normal Distribution with a Mean