crystalhoff2948
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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

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

[tex]\dfrac{142-156}9\approx-1.56[/tex]

[tex]\dfrac{165-156}{13}\approx0.69[/tex]

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.