Apples from an orchard have mean weight 70 grams and standard… Step by Step

Step by step

The question

Question: find the z-score of 82, when the mean is 70 and the SD is 8.

z-score of 82: mean 70, SD 8

A z-score tells how many SDs a number is from the mean.

z = how many SDs from the mean

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Write the formula

x minus the mean is how far x is from the mean.

Dividing by the SD counts how many SDs that is.

So z is x minus the mean, all over the SD.

z = x − meanSD

Careful!

Subtract first, then divide.

The whole top is divided by the SD.

Careful: not 82 − 708 ✗

2 Put the numbers in

The top first: 82 minus 70 is 12.

Then 12 divided by 8 is 1.5.

z = 82 − 708 = 128 = 1.5

3 Read it

82 on a number line with the SD marks.

The z numbers count the SDs.

So 82 is 1.5 SDs above the mean.

1.5 SDs above the mean

4 Check

Let's check: start at the mean and go 1.5 SDs.

70 plus 1.5 times 8 is 82.

So it is right!

70 + 1.5 × 8 = 82

5 Pick the choice

Our answer is z = 1.5.

That is choice C.

C) 1.5

6 Why not the others

A is 12.

Wrong: that is the distance from the mean: divide it by the SD.

A) 12 ✗ that is the distance from the mean: divide it by the SD

B is −1.5.

Wrong: 82 is above the mean: z is positive.

B) −1.5 ✗ 82 is above the mean: z is positive

D is 10.25.

Wrong: divided 82 by 8.

D) 10.25 ✗ divided 82 by 8

Let's look back.

First: write the formula.

Then: put the numbers in.

Then: read it.

Then: check.

Then: pick the choice.

Last: why not the others.

Answer