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
Suppose that you were running a research project on the items people packed into USPS #4 Priority Mail Box. You collect your data and do your analysis, and then realize that although you’ve worked with the net weights only the contents of the boxes are significant to your research. Suppose your measurements are in ounces. The median and mean are both 40 oz and the standard deviation is 5. If we find out that the boxes all weighed 3 oz and take that out, what are the new mean, median, and standard deviation?
37, 37, 5
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
Say the distribution has a mean, x¯=4 and deviation, s=10, and needs to be transformed so that the new mean and deviation are x¯=0.50 and s=2. What transformation(s) was/were performed?
multiplication of .2 and then -.3 added