A particular fruit's weights are normally distributed, with a mean of 756 gr. and a st dev of 14 gr The heaviest 20% of fruits weigh more than how many grams? Give your answer to the nearest gram.

Answer 1

If the mean is 756g then the heaviest 50% weigh more than 756g.

If we go 1 standard deviation heavier (756 + 14 = 770g) the normal distribution includes a further 34.1%, or 84.1%. This means the heaviest 15.9% of fruit weight more than 770g.

We need to find the place, slightly less than 1 standard deviation, where there is 20% of the curve left. A guesstimate would therefore be 765g.

The exact number of standard deviations is a z-score, and we need to look it up in a z-score table.

The z-score table gives the area under the normal curve to the left of z, so we need 20% or 0.2 (curve is symmetrical so either side is fine). This z score is 0.845.

The equation we need is weight = mean weight + number of SDs x standard deviation weight

The weight of the fruit is 756 + 0.845 x 14 = 767.83 or 768g.

Hence the heaviest 20% of fruit weights more than (or equal to) 768g.