Suppose you take a trip to Stars Hollow Apple Orchard. Stars Hollow Apple Orchar

Question

Suppose you take a trip to Stars Hollow Apple Orchard. Stars Hollow Apple Orchard is a magical place where the weight of the apples exactly follows a normal distribution! They grow two types of apples, Fuji and Gala.

• The weight of the Fuji apples is normally distributed with a mean of 91 grams and a standard deviation of 3 grams. Let X be the weight of a randomly selected Fuji apple.

• The weight of the Gala apples is normally distributed with a mean of 89 grams and a standard deviation of 4 grams. Let Y be the weight of a randomly selected Gala apple.

Suppose you pick four Gala apples at random. (Assume independence.) What is the probability their average weight is greater than 92 grams?

Explanation / Answer

For Gala apples, mean is 89 and standard deviation s is 4. z is defined as (x-mean)/s

thus P(x>92) =P(z>(92-89)/4) or P(z>0.75) or 1-P(z<0.75)

from normal distribution table we get 1-0.7734 =0.2266

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