Area under the curve
Area Under the Curve
(with real scores)
(with real scores)
Find the z score
(given the Percent)
(given the Percent)
Find area using real scores
Effects of Data Manipulation on Summary Statistics
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 more than less than 7 ounces?
.0013
100
If the highest score of a large data set increases by 100, which measure of center is most likely to change?
mean
200
p(z < 1.36)
.9131 or 91.31%
200
Mean = 40 and standard deviation is 13
p(z < 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 ounces
.0004 or .04%
200
If every value in a data set in increased by 5, the standard deviation will...
stay the same
300
p(z < 5.16)
1 or 100%
300
Mean = 40 and standard deviation is .8
p(x < 41)
.1056 or 10.56%
300
What z scores represent 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
What change transformed the blue curve into the red? Does this change the skew? 
standard deviation was multiplied by 2. No it is still normal
400
p(-2 < z < 1)
.8185 or 81.85%
400
Mean = 60 and standard deviation = 10 p(30 < x < 70)
.84 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
If the skew is positive is the mean above or below the median? (hint draw it)
The mean is above the median
500
p( 1.14 < z < 2.49)
.1207 or 12.07%
500
Mean = 40 and standard deviation = 7 p(35 < x < 60)
.7539 or 75.39%
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
X~N(0,1)
P(X<k) = 0.9573
Find k
k = 0.2483