Stat 104 – Homework 7
Due Thursday March 8, 2012
Reading:
February 28 – March 8
March 20 – March 27
Chapter 6
Chapter 7
Assignment:
1. Complete the following problems from the text: 6.3, 6.4, 6.7, 6.8, 6.43, and 6.44.
2. One thousand students in an introductory statistics class at Iowa State University were
asked: “How many siblings (brothers plus sisters) do you have?” A student is
selected at random from all the students who answered the question and let X = the
number of siblings the student has. Below is the probability distribution for X.
x
0
1
2
3
4
5
P(x)
0.040
0.343
0.339
0.167
0.054
0.028
x
6
7
8
9
10
11
P(x)
0.018
0.004
0.004
0.002
0.001
0.000
a)
b)
c)
d)
How do you know that P(x) is a probability distribution?
What is the probability that a randomly selected student is an “only child”?
What is the probability that a randomly selected student will have 1 or 2 siblings?
What is the probability that a randomly selected student will have 6 or more
siblings?
e) What is the mean number of siblings for students in this introductory statistics
class?
f) The standard deviation of the number of siblings for students in this introductory
statistics class is 1.35. What is the chance that the number of siblings a randomly
selected student has is within one standard deviation of the mean?
3. Have you ever noticed that some dogs seem to look like their owners? Michael Roy
and Nicholas Christenfeld, Psychology professors at the University of California San
Diego conducted a study 1 to see if people could match a dog with its owner. Pictures
of 25 purebred dogs and separate pictures of their owners were taken at dog parks in
Southern California. The pictures were taken so that the backgrounds were different
for the dog and its owner. Study participants were shown three pictures, one of the
owner and two of dogs. One of the dog pictures was actually that of the owner’s dog
and the other was of another random selected dog from the study. Study participants
were asked to indicate which of the two dogs most resembled the owner. Of the 25
1
Roy and Christenfeld (2004), “Do Dogs Resemble their Owners?” Psychological Science, 15 (5), 361363.
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owners of purebred dogs, 16 were matched with the correct dog. If dogs don’t
resemble their owners then the probability that an owner is matched with the correct
dog is 0.5 (participants are guessing). It is reasonable to assume that matching one
dog to one owner is independent of matching another dog to another owner.
a) Was this study an observational study or and experiment? Explain briefly.
b) Use JMP to calculate the probability distribution for the number of correct
matches for the set of 25 owners of purebred dogs. Have JMP round probabilities
to 4 decimal places.
c) Have JMP create a histogram of the probability distribution. Be sure the
histogram has a probability axis.
d) Describe the shape of the probability distribution.
e) What is the probability that there are exactly 16 owners are matched with the
correct dog?
f) What is the probability that 16 or more owners are matched with the correct dog?
g) What is the probability that 10 or fewer owners are matched with the correct dog?
h) What is the probability that 10 or fewer owners are matched with the incorrect
dog?
i) What is the mean number of owners matched with the correct dog, round to 1
decimal place? Explain how the mean number can be a fraction, even though the
number of correct matches is a whole number.
j) What is the standard deviation of the number of owners matched with the correct
dog, round to 2 decimal places?
k) What is the probability that the number of owners matched with the correct dog
falls between the mean minus two standard deviations and the mean plus two
standard deviations?
l) Turn in the JMP data table that contains the binomial probabilities as well as the
JMP output summarizing the distribution.
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