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A particular fruit's weights are normally distributed, with a mean of 273 grams and a standard...

A particular fruit's weights are normally distributed, with a mean of 273 grams and a standard deviation of 17 grams. The heaviest 4% of fruits weigh more than how many grams? Give your answer to the nearest gram.

Math   Statistics-And-Probability   
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Answer #1

Let W be the weight of a randomly selected fruit. Then W ~ N( = 273, = 17)

For the heaviest 4% of fruits , we need to find 1 - 0.04 = 0.96 = 96th percentile of the distribution.

From standard normal table, Z value for p = 0.96 is 1.75

The heaviest 4% of fruits weigh more than = + Z = 273 + 1.75 * 17 = 302.75

303 grams

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