Z-Score
Z = -1.0
Based on the empirical rule, what % of the data do you expect to fall within 1 standard deviation of the mean?
68%
Find Pr(Z<0)
Suppose the length of Python snakes follows a normal distribution with a mean of 100 inches and standard deviation of 10 inches.
What is the probability you would find a Python less than 80 inches?
Z= (80 - 100)/10 =-2.0
Pr (Z<-2.0) = 0.02275
or 0.025 if used Empirical rule
Find Pr(Z<0.42)
0.66276
What does a Z-score of 1.5 mean?
Using a normal distribution, what percentage of the data fall more than 2 standard deviations BELOW the mean?
2.5%
Find Pr(Z<1.0)
0.8413
Suppose the length of Python snakes follows a normal distribution with a mean of 100 inches and standard deviation of 10 inches.
What is the probability you would find a Python more than 110 inches?
Pr (Z>1.0) = 1-0.8413 = 0.1587
Or 0.16 (16%) if using Empirical Rule
In a normal distribution, what proportion of observations lie above the mean?
50%
Noah scores a 91 on the test. Calculate the Z-score corresponding to Noah's test grade.
Using a normal distribution, what percentage of the data fall 1 standard deviation ABOVE the mean?
16%
Find Pr(Z>-0.65)
0.74215
Suppose the length of Python snakes follows a normal distribution with a mean of 100 inches and standard deviation of 10 inches.
What is the probability you would find a Python less than 85 inches?
Z=(85-100)/10 = -1.50
Pr(Z<-1.50)=0.06681
Suppose the average cost of a gallon of gas follows a normal distribution with a mean of $3.50 and a standard deviation of $0.42.
What is the probability that a gallon of gas would cost $2.99 or less?
Pr (Z<-1.21)=0.11314
The average cost of a speeding ticket follows a normal distribution with a mean of $175.00 and a standard deviation of $45.
In Georgia, the average cost of a speeding ticket is $136. Find the Z-score associated with the average cost of a speeding ticket in Georgia.
Z=-0.87
Suppose the number of calories on a menu item at Cheesecake Factory follows a normal distribution with a mean of 1500 calories and a standard deviation of 500.
Approximately 68% of all menu item's calorie count falls between what two values?
1000 and 2000 calories
Find Pr(Z<-0.17)
0.43215
Suppose the length of Python snakes follows a normal distribution with a mean of 100 inches and standard deviation of 10 inches.
What is the probability you would find a Python more than 97 inches?
Z=(97-100)/10 = -0.3
Pr(Z>-0.3)=1-0.38209 = 0.61791
Suppose the average lifespan of a Bearded Dragon is 12.2 years with a standard deviation of 5.2 years.
What is the probability that Thor will live for at least 15 years?
Z=(15-12.2)/5.2 = 0.538
Pr(Z>0.54)=1-0.70540 = 0.29460
Dogs live on average 12 years with a SD of 3 years.
Cats live on average 14 years with a SD of 4 years.
What value is considered more "extreme", a cat that lives for 6 years or a dog that lives for 18 years?
Z-score (cat) = -2.0
They are equivalent.
16%
Find Pr(Z>1.64)
0.0505
Suppose the average college basketball arena holds 41,000 people with a standard deviation of 1,500.
What percentage of stadiums could hold more than 43,000 people?
Z=(43,000-41,000)/(1,500) = 1.33
Pr(Z>1.33)=1-0.90824=0.09176
Suppose the average lifespan of a Bearded Dragon is 12.2 years with a standard deviation of 5.2 years.
What is the probability that Thor will live less than 8 years?
Z=(8-12.2)/5.2 = -0.808
Pr(Z<-0.81) = 0.20897