Based on data from the National Health Survey, the average height in inches for women in the United States is 63.6 inches and the standard deviation is 2.5 inches. These are mux and sigmax, respectively. If we ask how many women are exactly some height, like 5'0" (60 inches) for example, the answer is assumed to be 0%. But if a woman says she is 5'0" tall, and she has measured herself correctly, she could be anywhere between 59.5 and 60.5 inches tall, which is to say 4' 11.5" and 5' 0.5". Let's find the z-scores for 59.5 and 60.5.

z(59.5) = (59.5-63.6)/2.5 = -1.64

z(59.5) = (59.5-63.6)/2.5 = -1.24

Using the Negative z-score table, we look up the percentages for each of these z-scores.

-1.64 -> .0505

-1.24 -> .1075

subtracting the percentages, we get .1075 - .0505 = .0570, which says 5.7% of American women list their height as 5'0".

Questions

1. What percentage of American women list their height as 5'1"?

2. What percentage of American women list their height as 5'2"?

3. What percentage of American women list their height as 5'3"?

4. What percentage of American women list their height as 5'4"?

5. What percentage of American women list their height as 5'5"?

6. What percentage of American women list their height as 5'6"?

7. What percentage of American women list their height as 5'7"?

8. What percentage of American women list their height as 5'8"?

9. What percentage of American women list their height as 5'9"?

Answers in the comments.

## Sunday, March 22, 2009

### Practice problems for population percentiles

Labels:
percentages,
practice problems,
standard deviation,
z-scores

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## 1 comment:

1. What percentage of American women list their height as 5'1"?

z(60.5) = -1.24

z(61.5) = -0.84

-0.84 -> .2005

-1.24 -> .1075

.2005 - .1075 = .0930 = 9.3%

2. What percentage of American women list their height as 5'2"?

z(61.5) = -0.84

z(62.5) = -0.44

-0.44 -> .3300

-0.84 -> .2005

.3300 - .2005 = .1295 = 12.95%

3. What percentage of American women list their height as 5'3"?

z(62.5) = -0.44

z(63.5) = -0.04

-0.44 -> .3300

-0.04 -> .4840

.4840 - .3300 = .1540 = 15.40%

4. What percentage of American women list their height as 5'4"?

z(63.5) = -0.04

z(64.5) = 0.36

-0.04 -> .4840

0.36 -> .6406

.6406 - .4840 = .1566 = 15.66%

5. What percentage of American women list their height as 5'5"?

z(64.5) = 0.36

z(65.5) = 0.76

0.36 -> .6406

0.76 -> .7764

.7764 - .6406 = .1358 = 13.58%

6. What percentage of American women list their height as 5'6"?

z(65.5) = 0.76

z(66.5) = 1.16

0.76 -> .7764

1.16 -> .8770

.8770 - .7764 = .1006 = 10.06%

7. What percentage of American women list their height as 5'7"?

z(66.5) = 1.16

z(67.5) = 1.56

1.16 -> .8770

1.56 -> .9406

.9406 - .8770 = .0636 = 6.36%

8. What percentage of American women list their height as 5'8"?

z(67.5) = 1.56

z(68.5) = 1.96

1.56 -> .9406

1.96 -> .9750

.9750 - .9406 = .0344 = 3.44%

9. What percentage of American women list their height as 5'9"?

z(68.5) = 1.96

z(69.5) = 2.36

1.96 -> .9750

2.36 -> .9909

.9909 - .9750 = .0159 = 1.59%

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