A particular fruit's weights are normally distributed, with a mean of 565 grams and a standard deviation of 31 grams. The heaviest 7% of fru

Question

A particular fruit's weights are normally distributed, with a mean of 565 grams and a standard deviation of 31 grams.

The heaviest 7% of fruits weigh more than how many grams?

Give your answer to the nearest gram.

Answer 1

W = weight of fruit W is N[565,31]

Q. A at what weight x is P(W>x) = .070?

Using inverse cumulative normal distribution function from calculator or computer

invNorm(1-.07,565,31) = 610.7495 g.

Rounded to nearest gram = 611 gram.

using Z table, find Z crit from table or calculator for area to left of Z > .9300

Z crit = 1.475791

use algebra to solve equation (x - 565)/31 = 1.475791 for x

hint x = (1.475791*31) + 565