Question

A particular fruit's weights are normally distributed, with a mean of 204 grams and a standard deviation of 5 grams. The heaviest 16% of fruits weigh more than how many grams? Give your answer to the nearest gram.

Answer #1

Let X be the random variable denoting the fruits weight.

X ~ N(204, 5) i.e. (X - 204)/5 ~ N(0,1)

Let the heaviest 16% of the fruits weigh more than 'a' grams.

Hence, P(X > a) = 0.16 i.e. P(X < a) = 1 - 0.16 = 0.84 i.e. P[(X - 204)/5 < (a - 204)/5] = 0.84 i.e. [(a - 204)/5] = 0.84 i.e. (a - 204)/5 = (0.84) = 0.994 i.e. a = 204 + (5 * 0.994) = 208.97 grams.

[(.) is the cdf of N(0,1)]

Hence, the heaviest 16% of fruits weigh more than 208.97 grams.

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