Final answer:
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.