Empirical Rule (68-95-99.7)
Area Under the Curve
Find the z score
(given the Percent)
Find area using real scores
Find real scores using area under the curve
100

Using the Empirical Rule:

What percent of data is within 1 standard deviation of the mean? (-1 SD to +1 SD)

68%

100

Mean = 23 and standard deviation is 1.5 

P(x > 21)

.9088 or 90.88%

100

What z score represents the 50th percentile

0

100

The average amount of hot fries in a bag is 8.5 ounces with a standard deviation of .5 ounces. What percent of bags have less than 7 ounces?

.0013 or 0.13%

100

Hot fries hold an average of 8.5 ounces in a bag with a standard deviation of .5 ounces. What is the weight of the bags in the 50th percentile?

8.5 ounces

200

Using the Empirical Rule:

What percent of data is below 2 standard deviations below the mean? (below -2 SD)

2.5%

200

Mean = 40 and standard deviation is 13 

P(x < 16)

.0324 or 3.24%

200
What z score represents the 90th percentile?
1.28
200

Cookie man cookies have a diameter of 2.5 inches with a standard deviation of .15 inches. What percent of cookies have a diameter of more than 3 inches?

.0004 or .04%

200

Cookie man cookies have a diameter of 2.5 inches with a standard deviation of .15 inches. What diameter represents the cookie, where 90% are smaller than this?

2.692 inches

300

Using the Empirical Rule:

Given a mean of 100 and a standard deviation of 10, what percent of data is between 80 and 110?

81.5%

300

Mean = 40 and standard deviation is .8 

P(x < 39)

.1056 or 10.56%

300

What z score represents the middle 60% of the data?

-.84 and .84

300

The average baby is born weighing 7.8 pounds with a standard deviation of 1 pound. What percent of babies weigh more than 9 pounds?

0.1151 or 11.51%

300

The average baby is born weighing 7.8 pounds with a standard deviation of 1 pound. What weight is in the 10th percentile?

6.52 pounds

400

Using the Empirical Rule:

Given a mean of 100 and a standard deviation of 10, 0.15% of data lies above what value?

130

400

N(60,10) 

P(32 < x < 66)

0.7232 and 72.32%

400
What are the z scores for the middle 95% of the data?
-1.96 and 1.96
400

Water bottles are supposed to hold 12 ounces with a standard deviation of .2 ounces. What percent of the water bottles hold between 12 and 12.6 ounces?

0.4987 or 49.87%

400

Water bottles are supposed to hold 12 ounces with a standard deviation of .2 ounces. What are the weights of bottles for the middle 50% of the data (25% on each side of the mean)?

11.886 and 12.114 ounces

500

Using the Empirical Rule:

Given a mean of 100 and a standard deviation of 10, what value is at the 16th percentile?

90

500

N(40,7)

P(50 < x < 60)

.0744 or 7.44%

500
What z score is associated with the top 15% of the data?
1.04
500

The average male is 72 inches tall (6 feet) with a standard deviation of 3.5 inches. What percent of men are over 7 feet tall? (be careful - how many inches is that?)

0.0003 or .03%

500

Find the mean if the standard deviation is 3 and

20 is at the 30th percentile. *Use the percentile and N(0,1) to find a z-score...*

do algebra using z-score=(value-mean)/SD

21.572

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