the range is to be all numbers between 0 and 2. Call the random number generated
Y
Then the density curve of the random variable
Y
has constant height between 0 and 2, and
height 0 elsewhere.
(a) What is the height of the density curve between 0 and 2? Draw a graph of the density
curve.
(b) Use your graph from (a) and the fact that probability is area under the curve to find
P
(
Y
≤
1.5).
(c) Find
P
(0.6 <
Y
< 1.7).
(d) Find
P
(
Y
≥
0.9).
4.66
Normal approximation for a sample proportion.
A sample survey contacted an
SRS of 663 registered voters in Oregon shortly after an election and asked respondents
whether they had voted. Voter records show that 56% of registered voters had actually
voted. We will see in the next chapter that in this situation the proportion
of the sample
who voted has approximately the Normal distribution with mean
= 0.56 and standard
deviation
σ
= 0.019.
(a) If the respondents answer truthfully, what is
P
(0.52
≤
p
^
≤
0.60)? This is the
probability that the statistic
estimates the parameter 0.56 within plus or minus 0.04.
(b) In fact, 72% of the respondents said they had voted (
p
^ = 0.72). If respondents answer
truthfully, what is
P
(
p
^
≥
0.72)? This probability is so small that it is good evidence that
some people who did not vote claimed that they did vote.
4.74
Mean of the distributions of errors.
Typographical and spelling errors can be
either “nonword errors” or “word errors.” A nonword error is not a real word, as when
“the” is typed as “teh.” A word error is a real word, but not the right word, as when
“lose” is typed as “loose.” When undergraduates are asked to write a 250-word essay
(without spell-checking), the number of nonword errors has the following distribution:
The number of word errors has this distribution:
.

Exercise Questions: Chapter 4
3
What are the mean numbers of nonword errors and word errors in an essay?
4.78
The effect of correlation.
Find the mean and standard deviation of the total number
of errors (nonword errors plus word errors) in an essay if the error counts have the
distributions given in
Exercise 4.74
and
(a) the counts of nonword and word errors are independent.