Statistics Question

Question

A particular fruit's weights are normally distributed, with a mean of 666 grams and a standard deviation of 19 grams.

The heaviest 10% of fruits weigh more than how many grams?

Give your answer to the nearest gram.

Answer 1

Hello Gaby,

The formula for Z Score is

Z score = ( x – µ ) / σ

Where x is the raw score, µ is the mean and σ is the standard deviation.

A particular fruit's weights are normally distributed, with a mean of 666 grams and a standard deviation of 19 grams.

So we already know that the mean is 666 grams and the standard deviation is 19 grams.

The heaviest 10% of fruits weigh more than how many grams?

This means you will need to find Z-Score corresponding to heaviest 10 percent of fruits which in your case is (1-.10) which means you have to find the z score corresponding with .9 area shaded to the left using a z table https://www.ztable.net/ which is z = 1.282

So substituting the values, we get

1.282=(x-666)/19

So just basic math this point forward

Hope this helps,

Samantha

Answer 2

First thing you would have to find is the z score corresponding to heaviest 10 percent of fruit. This can either be done using a z score table, excel or graphing calculator. In this case, you will be looking for .9 (1-.10) on the probability portion of the chart. The z score corresponding with .9 area shaded to the left is z = 1.282

Now use your z score formula to complete question.

z=(x-μ)/σ

Filling in for known values gives

1.282=(x-666)/19

Now just solve for x which equals 690.358 and rounded to the nearest gram is 690. The heaviest fruits weigh more than 690 grams.