The weights of eggs produced on a farm are normally distributed with a mean of 1.4 ounces and a standard deviation of 0.4 ounces. to be graded extra large, an egg must weigh at least 2 ounces. what is the probability that an egg from this farm will be graded extra large?

Since, X ~ N (1.4 oz, 0.4 oz)

Let X - weights of eggs produced on a farm

1. What are we looking for? Probability than an egg from this far will be graded extra-large. So we are looking for the probability greater than 2 ounces. So, it is P (X>2)

2. Look for the z value. The formula is z = X - mean divided by standard deviation. So in this problem, it it 2-1.4/0.4 = 1.5

3. Consult the Normal Distribution Table to find the corresponding z score of 1.5. In this case, it is. 9332. We want to find P (X>2) so this means we need the area to the right of X, so we need to deduct it to 1.

1 -.9332 = 0.0668 or 0.067

Thus, P (X>2) = 0.067