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7.1 Discrete & Continuous Random Variables
AP Stats
1. The number of customers that place orders at the drive-through window at a fast food restaurant each
hour is a discrete random variable. The data for a given 10 hour period is recorded below.
Hour
Customers per hour
1
8
2
4
3
9
4
12
5
7
6
16
7
4
8
7
9
9
10
12
a. In this case X = ___________________________
b. What values would X take on for this 10 hour period?
c. Make a frequency distribution for this 10 hour period only.
d. Make a probability distribution for this 10 hour period only. Do the probabilities bear out what
we know about probability distributions?
g. What is P(4 < X ≤ 9)?
e. What is P(X < 9)?
f.
What is P(X ≤ 9)?
h. Find the smallest number A for
which P(X < A) > 0.4.
2. On the board, put a tally mark next to the number of siblings you have (do not include yourself). Use
this information to make a probability distribution. Round to 3 decimal places if necessary.
a. Find P(X = 8)
b. Find P(X < 4)
c. Find the largest number A for which P(X < A) < 0.5.
0
3. Use the given spinner
a. Find P(X < .25)
b. Find P(X ≤ .75)
.75
.25
c. Find P(.25 < X < .75)
d. Find P(X = .25)
.50
4. You roll two dice and record the sum.
a. Make a probability distribution of the sum of two dice.
b. Make a probability histogram of the sum of two dice.
5. A probability density function is made up of two line segments. One starts at (0, 0) and goes to (3, .5).
The second goes from (3, .5) to a point (X, 0).
a. Sketch the distribution function, and determine what X has to be in order to be a legitimate
density curve.
b. Find P(0 < X ≤ 1.5).
c. Find P(X =3.5).
d. Find P(0 < X < 3.5).
e. Circle the correct option: X is an example of a (discrete) (continuous) random variable.