Area under the curve
Area Under the Curve
(with real scores)
Find the z score
(given the Percent)
Find area using real scores
Find real scores using area under the curve
100
p(z < -2.05)
.0202 or 2.02%
100
Mean = 23 and standard deviation is 1.5 p(x > 20)
.9772 or 97.72%
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

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
p(z < 1.36)
.9131 or 91.31%
200

Mean = 40 and standard deviation is 13 p(X < 16)

.0322 or 3.22%

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
p(z < 5.16)
1 or 100%
300

Mean = 40 and standard deviation is .8 p(x < 41)

.8944 or 89.44%

300
What z score represents the middle 50 of the data?
-.67 and .67
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?
.07%
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
p(-2 < z < 1)
.8185 or 81.85%
400

Mean = 60 and standard deviation = 10 p(30 < x < 70)

.8400 and 84%

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
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)?

11.866 and 12.134 ounces

500
p( 1.14 < z < 2.49)
.1207 or 12.07%
500

Mean = 40 and standard deviation = 7 p(35 < x < 60)

.7590 or 75.90%

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?
.03%
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
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