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Your Personal Tutor in Statistics © 2004 Jack Lubowsky Page 1 Calculating Areas Under the Normal Curve Percentage Calculations Your Personal Tutor in Statistics Click for Next

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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 decimal point 2 places to the LEFT. So…What is 55% as a decimal? 55% = 55.%. = 0.55 The leading zero is just a safety precaution to indicate that you just didn’t forget the leading digit. Click for Next

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Your Personal Tutor in Statistics © 2004 Jack Lubowsky Page 3 Calculating Percentages Move decimal 2 places to right So remember it this way… DECIMALPERCENT 0.3434 % Click for Next Move decimal 2 places to left DECIMALPERCENT 0.3434 %

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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%

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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 Next

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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?” -10 50 = -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? 15 50 = 0.30 = 30% The change is now

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