Math 3
Name_____________________
Unit 6 Review
1. Give an example of each of the following:
A. Discrete Variable
# of fish
# of marbles
# of people
B. Continuous Variable
Time
2. Make a table and histogram showing the probability distribution for the random variable.
X = the color of a marble chosen from a bag that contains 3 red marbles, 6 blue marbles, 2 green
marbles, and 4 orange marbles.
X
P(X)
Red
3/15
Blue
6/15
Green
2/15
Orange
4/15
3. Calculate the probability of each of the following:
A. Tossing a normal coin and the coin lands on tails 8 out of 28 times.
0.012
B. You random guess at a 35 question test with each problem having choices (A, B, C, D, or E). What is
the probability that you get 10 questions correct?
0.071
4. Use the fact that 12% of people wear contact lenses. Consider a high school with 2023 students:
A. What is the probability that at least 151 students wear contact lenses?
100% or 1
B. What is the probability that at most 230 students wear contact lenses?
0.202
Make a table and a histogram showing the probability distribution for the random variable. Describe the
distribution as either symmetric or skewed.
5) S = the sum of two dice
Calculate the probability of tossing a coin 20 times and getting the given number of heads.
6) 3
0.0011
7) 12
0.12
Calculate the probability of k successes for a binomial experiment consisting of n trials with probability p of
success on each trial.
8) k ≥ 3, n = 7, p = 0.25
0.244
9) k ≤ 6, n = 11, p = 0.43
0.859
A normal distribution has mean x and standard deviation σ. Find the indicated probability for a randomly
selected x-value from the distribution.
10) P( x ≥ ̅𝑥) = 0.50 or 50%
11) P ( 𝑥̅ -σ≤ x ≤ 𝑥̅ +2σ) = 81.6%
A normal distribution has a mean of 18 and a standard deviation of 3. Find the probability that a randomly
selected x-value from the distribution is in the given interval.
12) Between 18 and 21
0.34
13) Between 15 and 24
0.819
14) At least 21
0.159
15) At most 12
0.0228
Find the mean and standard deviation of a normal distribution that approximates the binomial distribution
with n trials and probability p of success on each trial.
16) n = 20, p = 0.4
𝑥̅ = 8
σ = 2.19
18) n = 80, p = 0.7
𝑥̅ = 56
σ = 4.10
17) n = 50, p = 0.2
𝑥̅ = 10
σ = 2.83
19) n = 100, p = 0.75
𝑥̅ = 75
σ = 4.33
In Exercises 20 – 22 , use the fact that approximately 9% of U.S.children have asthma. Consider an elementary
school with 500 children.
20) What is the probability that at least 45 children have asthma?
0.50
22) What is the probability that at most 39 children have asthma?
0.174
23) What is the probability that at most 51 children have asthma?
0.826