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

Jayla Lawrence · Accepted Answer

Final Answer : B, Explanation :  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 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

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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) 0.0000B) 0.0019C) 0.1814D) 0.2033

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Learning Objectives

Learning Objectives

Related questions

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