Question

A candy maker produces mints that have a label weight of 21 grams. Assume the distribution of the weight of these mints is N(21.4, 0.09). What is the probability that the weight of a mint is greater than 22.07 grams?

Answer 1

To find the probability of the weight being greater than 22.07 grams for the given distribution, calculate the z-score and find the corresponding area under the standard normal distribution curve.

Step-by-step explanation:

To find the probability that the weight of a mint is greater than 22.07 grams, we need to calculate the z-score and then find the corresponding area under the standard normal distribution curve.

First, calculate the z-score using the formula:

z = (x - μ) / σ

In this case, x = 22.07 grams, μ = 21.4 grams, and σ = 0.09 grams. Substituting these values into the formula:

z = (22.07 - 21.4) / 0.09 = 7.4444

Next, we can use a standard normal distribution table or a calculator to find the area to the right of the z-score:

P(X > 22.07 grams) = P(Z > 7.4444) ≈ 0

Therefore, the probability that the weight of a mint is greater than 22.07 grams is approximately 0.