Percentile
Test Scores:
62, 68, 70, 70, 74, 78, 82, 85, 85, 90
What percentile is the person who scored an 82?
70th percentile
A normal distribution has a mean of 15 and a standard deviation of 3. What is the value that is 3 negative standard deviations away from the mean?
6
What is the formula for z-score?
Data point - Mean divided by Standard deviation
Cookie Monster's cookies have a diameter of 5.5 inches with a standard deviation of .25 inches. What percent of cookies have a diameter of more than 5.3 inches?
78.8%
The age of teachers is normally distributed. The average age of a teacher is 108 years with standard deviation 22 years. The 95 percentile of teachers are how old?
144.19 years old
Student Height:
60, 62, 64, 65, 66, 67, 68, 70, 71, 73
Who is in the 40th percentile?
Person who is 65 inches
A normal distribution has a mean of 8 and a standard deviation of 2. What is the value that is plus 2 standard deviations away from the mean?
12
A data set has a mean of 78 and a standard deviation of 9.
What is the z-score of a value of 86?
0.8889
The average amount of fries in a bag is 8.5 ounces with a standard deviation of .5 ounces. What percent of bags have less than 7 ounces?
0.13%
The reaction times of professional gamers are normally distributed with a mean of 250 milliseconds and a standard deviation of 30 milliseconds. What reaction time marks the 25th percentile of players?
229.77 milliseconds
Books Read Over the Summer:
0, 1, 1, 2, 2, 3, 4, 5, 5, 5, 6, 6, 8, 8, 8, 9, 10
What percentile is the person who read 8 books?
The number of standard deviations a point is from the mean
A normal distribution has a mean of 24 and a standard deviation of 6. 68% of the values of this distribution fall between what two data values?
What is 18 and 30?
A student scored a 78 on a math test with a mean of 70 and a standard deviation of 8.
The same student scored an 85 on a science test with a mean of 80 and a standard deviation of 4.
On which test did the student perform better relative to the class? Explain with a z-score
Science. 1.25 is a higher distance from mean.
Water bottles are supposed to hold an average of 12 ounces with a standard deviation of .2 ounces. What percent of the water bottles hold between 12 and 12.6 ounces?
49.87%
The heights of adult men are approximately normally distributed with a mean of 70 inches and a standard deviation of 3 inches.
Approximately what height separates the tallest 16% of adult men from the rest?
72.98 inches
Commute Time to School:
5, 7, 9, 10, 12, 15, 18, 20, 22, 30, 35, 35, 36, 37, 37, 38, 40, 41, 45, 48
How many students are in the 60th percentile?
12
A normal distribution has a mean of 100 and a standard deviation of 10. What is the percentage of data values that fall between the values of 70 and 90?
15.85
A student ran two races:
In the 100-meter dash, the student ran a time of 13.2 seconds. The mean time was 14.0 with a standard deviation of 0.8.
In the 200-meter dash, the student ran a time of 28.5 seconds. The mean time was 30.0 with a standard deviation of 1.2.
Determine in which race the student performed better relative to the group.
100 meter dash. -1 is less far from the mean than -1.25
The average newborn weight is 7.5 pounds with a standard deviation of 1.1 pounds. If anything above 10 or below 6 pounds is considered unusual, what percentage of newborns are considered unusual?
9.8%
The scores on a statewide math assessment are normally distributed with a mean of 78 and a standard deviation of 6.
What is the minimum score required to be in the top 2.5% of test-takers?
89.76
Screentime:
1.2, 1.5, 2.0, 2.3, 2.8, 3.1, 3.5, 4.0, 4.6, 5.2, 6, 6.5, 7, 7.5, 7.5, 7.8, 9
How many more hours did the person in the 88th percentile have than the person in the 29th percentile?
4.7 hours
A normal distribution has a mean of 250 and a standard deviation of 12.5. What is the percentage of data values that fall between the values of 212.5 and 275?
97.35
Three students took different standardized exams:
Student A: Score = 88, Mean = 75, Standard Deviation = 10
Student B: Score = 92, Mean = 85, Standard Deviation = 5
Student C: Score = 78, Mean = 70, Standard Deviation = 4
Rank the students from highest to lowest performance relative to their group.
C, B, A
2000 students took an exam. The scores on the exam are approximately normally distributed with a mean of 500 and a standard deviation of 100. Scores above 650 are considered for honors. What number (not percentage!) of students will receive honors?
133.6 (134) students.
The average length of time it takes to run a race is 56 minutes with standard deviation 3.2 minutes. The fastest 1% of runners finish within how many minutes? (Careful with the wording of this!)
48.56 minutes