Download Section 3.4

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Section________
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Homework #3
This homework is due WEDNESDAY, Feb. 12th or Thursday, Feb. 13th.
Note: there is NO data for this homework. You can still use the Open Lab Hours: Sunday 27,
MondayThursday 5:308 and Wednesday 123, in BLOC 161 for questions and help. Note: there is no longer
help Mondays 25. Most of these problems are short anwers. From your text, Introduction to the Practice of
Statistics (Fourth Edition):
Section 3.1
1. 3.4
Section 3.2
2. 3.16
Section 3.3
3. 3.48
Section 3.4
4. First answer:
 Why do we take samples?
 What makes a ‘good’ sample?
 How does taking a bigger (increasing the sample size, n) sample help?
 Why is randomization so important in statistical inference?
 Define population parameter and sample statistic and explain how we use each of them in statistics.
5. 3.60
6. 3.64
Section 4.1
7. Using the Probability applet (found under Student Resources  Statistical Applets on the IPS homepage,
http://bcs.whfreeman.com/ips4e which can also be found through the Stat30X Homepage  Applets 
Introduction to the Practice of Statistics, Applets), exercise 4.8
Section 4.3
8. exercise 4.50
9. exercise 4.52
More on Normals
There multiple members of the Normal Family. Five
are displayed in the graph at the right.
Definition of the notation Z~ N( 0, 12):
Z is the random variable for which we are defining
a distribution.
~ means “is distributed as,” and must be followed by some
probability distribution. (remember SHAPE, CENTER,
SPREAD define a distribution)
N means the random variable is normally distributed, the shape
is a bell-shaped curve.
0 means Z has mean 0, so the center is 0.
12 means Z has a standard deviation of 1, so the spread is 1.
NOTE: Although the textbook uses the standard deviation
as the second number in the parentheses, we will always
use the variance and will always write it as the sd2.
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10. Consider the population of all one-gallon cans of dusty rose paint manufactured by a particular paint
company. Suppose that a normal distribution with mean  = 5 ml and standard deviation  = 0.2 ml is a
reasonable model for the distribution of the variable x = amount of red dye in the paint mixture. Use the normal
distribution model to calculate the following probabilities. NOTE: X ~ N(  = 5, 2 = 0.22 )
a. P( X  5.4) =
b. P(4.6 < X < 5.2) =
c. P( X > 4.5) =
11. A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the variable x = actual
capacity of a randomly selected tank has a distribution that is well approximated by a normal curve with mean
15.0 gal and standard deviation 0.1 gal. NOTE: X ~ N(  = 15, 2 = 0.12 )
a. What is the probability that a randomly selected tank will hold at most 14.8 gal?
b. What is the probability that a randomly selected tank will hold between 14.7 and 15.1 gal?
c. If two such tanks are independently selected, what is the probaility that both hold at most 15 gal?
Section 4.4
12. exercise 4.67
13. exercise 4.82