Download 6.1 HW WS

Name:_________________________
AP Stats/ __________
Date: ___________ Date Due:_____________
AP Statistics
6.1 Homework Worksheet
Discrete and Continuous Random Variables
Please show all work on a separate piece of paper
1) Toss a coin 4 times. Let 𝑋 = 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 ℎ𝑒𝑎𝑑𝑠 you get
a. Find the probability distribution of X
b. Find 𝑃(𝑋 ≤ 3) and interpret the result
2) Suppose you roll a pair of fair, six-sided dice. Let T = the sum of the spots showing on the up-faces (in
other words, the sum of the two die).
a. Find the probability distribution of T
b. Find 𝑃(𝑇 ≥ 5 ) and interpret the result.
3) In an experiment on the behavior of young children, each subject is placed in an area of five toys. Past
experiments have shown that the probability distribution of the number X of toys played with by a
randomly selected subject is as follows:
Number of Toys
0
1
2
3
4
5
Probability
a.
b.
c.
d.
.03
.16
.30
.23
.17
.11
Find 𝑃( 𝑝𝑙𝑎𝑦𝑠 𝑤𝑖𝑡ℎ 𝑎𝑡 𝑚𝑜𝑠𝑡 𝑡𝑤𝑜 𝑡𝑜𝑦𝑠)
Describe the event 𝑋 > 3 in words. What is its probability? What is the probability that 𝑋 ≥ 3?
Calculate the mean of the random variable X and interpret this result in context.
Calculate the standard deviation of the random variable X and interpret this result in context.
4) The normal distribution with mean 𝜇 = 6.8 and 𝜎 = 1.6 is a good description of the Iowa Test of Basic
Skills (ITBS) vocabulary scores of seventh-grade students in Gary, Indiana. Call the score of randomly
chosen student X for short. Find 𝑃(𝑋 ≥ 9) and interpret the result.
5) The weights of three year old females closely follow a Normal distribution with a mean of 30.7 pounds
and a standard deviation of 3.6 pounds. Randomly choose one three year old female and call her
weight X.
a. Find the probability that the randomly selected three year old female weighs at least 30
pounds.
b. Find the probability that the randomly selected three year old female weighs at between 27.1
and 34.3 pounds.
Name:_________________________
AP Stats/ __________
Date: ___________ Date Due:_____________
6) Choose a person aged 19 to 25 years at random and ask, “In the past seven days, how many times did
you go to an exercise or fitness center or work out?” Call the response Y for short. Based on a large
sample survey, here is the probability model for the answers you get
Days
0
1
2
3
4
5
6
7
Probability .68
.05
.07
.08
.05
.04
.01
.02
a. Show that this is legitimate probability distribution.
b. Describe the event 𝑌 < 7 in words. What is 𝑃(𝑌 < 7)?
c. Make a histogram of the probability distribution, describe what you see.
Consider the events 𝐴 = 𝑤𝑜𝑟𝑘𝑠 𝑜𝑢𝑡 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑐𝑒 and 𝐵 = 𝑤𝑜𝑟𝑘𝑠 𝑜𝑢𝑡 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 5 𝑡𝑖𝑚𝑒𝑠 𝑝𝑒𝑟 𝑤𝑒𝑒𝑘
d. What outcomes make up the event A, what is P(A)?
e. What outcomes make up event B, what is P(B)?