The weights of extra large eggs have a normal distribution with a mean of one ounce and a standard deviation of 0.1 ounces. The probability that a dozen eggs weighs more than 13 ounces is closest to...?

you might want to look at my answer to Belinda, 5 posts back

Her problem and yours are the same style

For your question you have to divide 13 by 12 to get the weight of one egg.

To find the probability that a dozen eggs weighs more than 13 ounces, we need to calculate the probability that the mean weight of a dozen eggs is greater than 13 ounces.

First, let's calculate the mean weight of a dozen eggs. Since there are 12 eggs in a dozen, the mean weight of a dozen eggs would be 12 times the mean weight of a single egg. Given that the mean weight of a single egg is 1 ounce, the mean weight of a dozen eggs would be 12 * 1 = 12 ounces.

Next, let's calculate the standard deviation of a dozen eggs. Since the standard deviation of a single egg is 0.1 ounces, the standard deviation of a dozen eggs would be the square root of (12^2 * 0.1^2), which simplifies to sqrt(144 * 0.01) = sqrt(1.44) = 1.2 ounces.

Now, we can use the properties of the normal distribution to find the probability that the weight of a dozen eggs is greater than 13 ounces. We will calculate the z-score, which measures how many standard deviations away from the mean a value is. The z-score is given by the formula:

z = (x - μ) / σ

where x is the value we are interested in (13 ounces), μ is the mean (12 ounces), and σ is the standard deviation (1.2 ounces). Plugging in the values, we get:

z = (13 - 12) / 1.2 = 1 / 1.2 = 0.8333

Now, we can use a standard normal distribution table or a calculator to find the probability associated with this z-score. The probability that a random z-score from a standard normal distribution is greater than 0.8333 is approximately 0.203.

However, since we are dealing with the weight of a dozen eggs, which is a continuous variable, we need to account for the fact that the weight cannot be exactly equal to 13 ounces. We need to consider the area under the curve to the right of the value 13 ounces. Since the normal distribution is symmetric, we can find the probability by subtracting the probability associated with the z-score from 0.5:

probability = 0.5 - 0.203 = 0.297

Therefore, the probability that a dozen eggs weighs more than 13 ounces is closest to 0.297.