Your Personal Tutor in Statistics © 2004 Jack Lubowsky Page 1

Calculating Areas Under the Normal Curve

PercentageCalculations

YourPersonalTutor

inStatistics

Click for Next

Your Personal Tutor in Statistics © 2004 Jack Lubowsky Page 2

We are all familiar with certain percentages.

Calculating Percentages

Click for Next

For example,50% is the same as 1/2.

Why?The word “per/cent” means “per hundred.”

So 50% = 50/100 which equals 0.50,

so 50% also equals 0.50.

Don’t believe me?

Go ahead.

Put it in your calculator.

OK, so 50% and 0.50 are exactly the same.

Likewise, 38% and 0.38 are exactly the same.

Going from % to decimal moves the decimalpoint 2 places to the LEFT.

So…What is 55% as a decimal?

55% = 55.% . = 0.55

The leading zero is just a safety precautionto indicate that you just didn’t forget theleading digit.

Click for Next

Click for Next

Your Personal Tutor in Statistics © 2004 Jack Lubowsky Page 3

Calculating Percentages

Move decimal 2 places to right

So remember it this way…

DECIMAL PERCENT

0.34 34 %

Click for Next

Move decimal 2 places to left

DECIMAL PERCENT

0.34 34 %

Your Personal Tutor in Statistics © 2004 Jack Lubowsky Page 4

Calculating Percentages

Now to practice.

Click for Next

Answer the question then click to see the answer.

Convert 45% to decimal. 0.45

Convert 38.34% to decimal.0.3834

Convert 0.005% to decimal.0.00005

Convert 238.1% to decimal.02.381

Let’s continue.

Convert 0.45 to percent. 45%

Convert 7.574 to percent. 757.4%

Convert 0.005 to percent. 0.5%

Convert .3875 to percent. 38.75%

Your Personal Tutor in Statistics © 2004 Jack Lubowsky Page 5

Calculating Percentages

Click for Next

Using Percentages

To take the percent of a number,convert the percent to a decimal and multiply.

For example,A city with a population of 3.8 million people grew by 3.65%. How many people were added?

3.65% Convert to decimal,

0.0365 x 3.8 = .1387 million people

In another city the population decreased by 4%.

If the initial population was 2.6 million, what was the population after the decrease?

There is more than one way to do this problem.1. You could convert 4% to decimal 0.04 and then multiply 0.04 x 2.6 = 0.104 million.

2. If the population decreased by 4%, then it will become 96% of what it was initially.

So 96% of 2.6 million is 0.96 x 2.6 = 2.496 million

Ready to do some more problems?

Then the population is 2.6 – 0.104 = 2.496 . . . or . . .

0.0365

Click for NextClick for Next

Your Personal Tutor in Statistics © 2004 Jack Lubowsky Page 6

$50

Calculating Percentages

Click for Next

Using Percentages

Now we will explore how percentages are used.

Percentages are a way of comparing two numbers.

is reduced by $10,

For example,

So we have a change of -20%.

The original price was

If a $50 item

what is the percent change?

$40

The question really asks, “what was the change compared to the original price?”

-1050 = -0.20 = -20%The change was

So we have a change of 30%.

The original price was

If the price had gone up to $65, what would the percent change have been?

1550

= 0.30 = 30%The change is now