Percentiles
Alex scored in the 79th percentile of an exam that was taken in his statistics class. What does this mean?
Alex did the same as or better than 79% of students who took the stats exam.
The average height for 12 year old females is 59 inches, and the standard deviation is 1.7 inches. Sarah is 54 inches tall. What is Sarah’s z-score?
Sarah’s z-score is -2.94
What is the percent rule for a normal curve distribution?
The 68-95-99.7 rule
What is the z-score for the 63rd percentile under the standard normal distribution?
Z = 0.33
A variable is normally distributed with mean 10 and standard deviation 3. Find the percentage of all possible values of the variable that are at most 17.5.
99.38%
There were 312 students who took an exam. Nick scored the same as or better than 243 of them. What is Nick’s percentile?
Nick scores in the 78th Percentile
The average height of 12 year old males is 58 inches, with a standard deviation of 2.1 inches. Billy’s z-score is 2.38. How tall is Billy?
Billy is 63 inches tall
An entomologist has a colony of spiders in his lab. There are 1200 adult spiders in the colony, and their weights are normally distributed with mean 15 grams and standard deviation 3 grams. What percent of spiders weigh less than 18 grams?
84% of spiders weigh less than 18 grams
What is the area to the left of -1.38 under a standard normal distribution?
0.08379
A variable is normally distributed with mean 10 and standard deviation 3. Find the percentage of all possible values of the variable that are at least 8.
74.54%
312 students took an exam. Lisa fell into the 93rd percentile. Approximately how many students did she outscore?
Lisa outscored 290 students
Teresa scored a 93 on her exam, giving her a z-score of 2.19. If the standard deviation of the class was 3.6, what was the class average?
The class average was 85.116%
An entomologist has a colony of spiders in his lab. There are 1200 adult spiders in the colony, and their weights are normally distributed with mean 12 grams and standard deviation 1.5 grams. What percent of spiders weigh more than 13.5 grams?
16% of spiders weigh more than 13.5 grams
What is the area to the right of 0.83 under the standard normal distribution?
0.20327
A variable is normally distributed with mean 10 and standard deviation 3. Find the percentage of all possible values of the variable that are between 6 and 7.
6.74%
Stan scored the same as or better than 156 other students on an exam, putting him in the 43rd percentile. How many students took the exam?
Approximately 363 students took the exam
Aaron has a salary of $54,000, giving him a z-score of 0.213. If the mean salary was $53,000, what would be the standard deviation?
The standard deviation is $4,694.84
An entomologist has a colony of spiders in his lab. There are 1200 adult spiders in the colony, and their weights are normally distributed with mean 15 grams and standard deviation 3 grams. What percent of spiders weigh between 9 grams and 18 grams?
81.5% of spiders weigh between 9 grams and 18 grams
What is the area between 1.92 and -2.16 under the standard normal distribution?
.95718
500 students took a test. The average score for this test is 68 with a standard deviation of 10. If 60 and below is considered failing, how many students failed the exam?
106 students
Alex took an exam with 243 other students. He scored in the 84th percentile. How many students outscored Alex?
39 students outscored Alex
Sofia scores 600 on the SAT math test. The distribution of SAT scores in the population is roughly symmetric and single-peaked with mean 500 and standard deviation 100. Jim takes the ACT Math test and scores 26. ACT scores follow a symmetric, single-peaked distribution with mean 18 and standard deviation 6. Assuming both tests measure the same kind of ability, who did better?
Sofia has a z-score of 1.60, while Jim has a z-score of 1.33. Therefore, Sofia performed slightly better.
An entomologist has a colony of spiders in his lab. There are 1200 adult spiders in the colony, and their weights are normally distributed with mean 15 grams and standard deviation 3 grams. How many spiders weigh between 9 grams and 21 grams?
1,140 spiders weigh between 9 grams and 21 grams.
The area under a standard normal distribution is 0.43, bound between a lower z-score of _____ and an upper z-score of 0.64. Determine the lower z-score.
-0.50
A variable is normally distributed with mean 10 and standard deviation 3. Find the value that 35% of all possible values of the variable exceed.
11.17