Normal Distribution

Area under the curve

100

P(Z < -2.05)

0.0202 or 2.02%

200

P(Z < 1.36)

0.9131 or 91.31%

300

P(Z < 5.16)

1 or 100%

400

P(-2 < Z < 1)

0.8185 or 81.85%

500

P( 1.14 < Z < 2.49)

0.1207 or 12.07%

Area Under the Curve(with real scores)

100

Mean = 23 and standard deviation is 1.5 

P(x > 20)

0.9772 or 97.72%

200

Mean = 40 and standard deviation is 13 

P(z < 16)

0.0322 or 3.22%

300

Mean = 40 and standard deviation is 0.8 

P(x < 41)

0.1056 or 10.56%

400

Mean = 60 and standard deviation = 10 

P(30 < x < 70)

0.84 and 84%

500

Mean = 40 and standard deviation = 7 

P(35 < x < 60)

0.7539 or 75.39%

Find the z score(given the Percent)

100

What z score represents the 50th percentile

0

200

What z score represents the 90th percentile?

1.28

300

What z score represents the middle 50 of the data?

-0.67 and 0.67

400

What are the Z scores for the middle 95% of the data?

-1.96 and 1.96

500

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

1.04

Find area using real scores

100

The average amount of hot fries in a bag is 8.5 ounces with a standard deviation of 0.5 ounces. What percent of bags have more than less than 7 ounces?

0.0013 or 0.13%

200

Cookie man cookies have a diameter of 2.5 inches with a standard deviation of 0.15 inches. What percent of cookies have a diameter of more than 3 ounces

0.0004 or 0.04%

300

The average baby is born weighing 7.8 pounds with a standard deviation of 1 pound. What percent of babies weigh more than 11 pounds?

0.07%

400

Water bottles are supposed to hold 12 ounces with a standard deviation of 0.2 ounces. What percent of the water bottles hold between 12 and 12.6 ounces

49.87%

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?

0.03%

Find real scores using area under the curve

100

Hot fries hold an average of 8.5 ounces in a bag with a standard deviation of 0.5 ounces. What is the weight of the bags in the 50th percentile?

8.5 ounces

200

Cookie man cookies have a diameter of 2.5 inches with a standard deviation of 0.15 inches. What diameter represents the cookie, where 90% are smaller than this?

2.692 inches

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

Water bottles are supposed to hold 12 ounces with a standard deviation of 0.2 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

The average male is 72 inches tall (6 feet) with a standard deviation of 3.5 inches. What heights represent the middle 50% of the data?

69.655 to 74.345 inches