The mean height in a sample is 152 cm with a margin of error of 3… Step by Step

Step by step

The question

Question: The mean height in a sample is 152 cm with a margin of error of 3 cm.

Is 150 cm a plausible value for the mean?

1 What the margin means

152 cm comes from a sample: only some of the people.

The true value for everyone can be a bit different.

The margin of error, 3 cm, says how far it can be.

152 ± 3

± means plus or minus: we go 3 cm down and 3 cm up.

The true value is likely in between.

± = plus or minus

true value: likely within 3 of 152

2 Lowest and highest

The lowest likely value: 152 minus 3 is 149.

lowest = 152 − 3 = 149

The highest: 152 plus 3 is 155.

highest = 152 + 3 = 155

3 Draw it

A number line from 147 to 157: a bit of room on each side.

The likely values go from 149 to 155.

We colour them green.

152, the sample's answer, is right in the middle.

Now 150, the value in the question.

We mark it in red.

4 Inside or outside

150 is between 149 and 155: inside the green part.

= 149 ≤ 150 ≤ 155

Careful!

Plausible means likely.

It does not mean the true value is 150 for sure.

Careful: plausible = likely, not sure

So yes: 150 cm is a plausible value.

= yes, 150 is plausible

5 Check

Let's check another way: how far is 150 from 152?

152 minus 150 is 2.

That is within the margin, 3.

So it is right!

152 − 150 = 2, 2 ≤ 3

Let's look back.

First: what the margin means.

Then: lowest and highest.

Then: draw it.

Then: inside or outside.

Last: check.

Answer