Question

3. The weights of apples in a shipment from Al's Orchards are normally distributed with a mean of 142 grams and a standard deviation of 9 grams. The weights of apples in a shipment from Zippy's Orchards are normally distributed with a mean of 165 grams and a standard deviation of 13 grams.
A rotten apple has a mean of 156 grams. Was it more likely to come from Al's or from Zippy's? Use z-scores to explain. Show your work

Answer 1

The z scores corresponding to the mean weight of a rotten apple relative to the apples from either orchard are, respectively,

$\dfrac{142-156}9\approx-1.56$

$\dfrac{165-156}{13}\approx0.69$

The mean for the standard normal distribution is 0, which means that z scores closer to 0 represent data points that are more likely to occur. Therefore it's reasonable to believe that rotten apples occur more often in shipments from Zippy's.