Empirical rule
A bell-shaped distribution has a mean of 50 and a standard deviation of 5. Approximately what percentage of values fall between 45 and 55?
Answer: 68%
The mean score is 70, with a standard deviation of 5. A student scores 80. Find the z-score.
z=2
A fair coin is tossed twice. Write the complete sample space.
HH, HT, TH, TT
A teacher selects 2 students from a group of 5 to represent the class. How many different groups can be selected?
=10
From 5 students, a president and vice president are selected. How many different outcomes are possible?
=20
The average exam score is 72 with a standard deviation of 4. Scores are approximately bell-shaped. Approximately what percentage of scores fall between 64 and 80?
Answer: 95%
The mean score is 60, with a standard deviation of 8. A student scores 48. Find the z-score.
z=-1.5
A fair coin is tossed 3 times. What is the probability of getting exactly 2 heads?
P=8/3
A committee of 3 people is selected from 7 people. How many different committees are possible?
=35
Six runners compete in a race. In how many different ways can 1st, 2nd, and 3rd place be awarded?
=120
A bell-shaped distribution has a mean of 100 and a standard deviation of 8. Between what two values will approximately 99.7% of the observations fall?
Answer: 76 and 124
A student has a z-score of −1.25. What does this tell you about the student's score?
The student's score is 1.25 standard deviations below the mean.
A fair coin is tossed 3 times. What is the probability of getting at least 2 tails?
P=1/2
A pizza shop has 8 toppings. You want to choose 4 different toppings. How many different 4-topping combinations are possible?
=70
There are 7 different books, but you only have room for 4 books on a shelf. How many different arrangements of 4 books are possible?
=840
On Exam A, the mean is 75 with a standard deviation of 10. Maya scores 91.
On Exam B, the mean is 500 with a standard deviation of 100. Noah scores 640.
Who performed better relative to their population?
NOAH=1.4
MAYA=1.6
Maya performed better relative to her population.
A fair coin is tossed 3 times. What is the probability that all three outcomes are the same?
P=1/4
A lottery requires you to select 5 numbers from 1 through 20. Order does not matter. If you buy one ticket, what is the probability that you select all 5 winning numbers?
P=1/15,504
combination or permutation? Then determine how many different outcomes are possible.
=336