Step 1 :The problem is asking for the number of peaches that weigh more than 13.2 ounces. This is a problem of normal distribution. We know that the mean weight of the peaches is 16 ounces and the standard deviation is 0.8 ounce.
Step 2 :We can use the z-score formula to find the z-score for 13.2 ounces. The z-score is a measure of how many standard deviations an element is from the mean. The formula for the z-score is: \(z = \frac{X - \mu}{\sigma}\) where: \(X\) is the value we are interested in (13.2 ounces in this case), \(\mu\) is the mean (16 ounces), \(\sigma\) is the standard deviation (0.8 ounce).
Step 3 :Substituting the given values into the z-score formula, we get: \(z = \frac{13.2 - 16}{0.8} = -3.5\)
Step 4 :Once we have the z-score, we can use a z-table to find the proportion of peaches that weigh more than 13.2 ounces. The z-table gives us the area under the curve to the left of the given z-score. Since we want the proportion of peaches that weigh more than 13.2 ounces, we need to subtract the area under the curve to the left of the z-score from 1. This gives us a proportion of approximately 0.9997673709209645.
Step 5 :Finally, we multiply this proportion by the total number of peaches (1000) to get the expected number of peaches that weigh more than 13.2 ounces. This gives us: \(1000 \times 0.9997673709209645 = 999.7673709209645\)
Step 6 :Rounding to the nearest whole number, we get approximately 1000 peaches.
Step 7 :Final Answer: The number of peaches expected to have weights of more than 13.2 ounces is approximately \(\boxed{1000}\).