# Calculating the probability using mean and standard deviation.

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The weights of medium oranges packaged by an orchard are normally distributed with a mean of 14 ounces and a standard deviation of 2 ounces. The weights of large oranges are normally distributed with a mean of 18 ounces and a standard deviation of 3 ounces. If we select, at random, one each of the medium and large oranges, determine the probability the medium orange weighs more than the large.

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#### Solution Preview

Since both are normal distribution, the Weight Difference should also be a normal distribution.

Let's find the normal distribution of Weight Difference:

Its mean ...

#### Solution Summary

The solution addresses the weights of medium oranges packaged by an orchard are normally distributed with a mean of 14 ounces and a standard deviation of 2 ounces.

$2.49