STAT 350 Assignment 6 Solutions
(40 points)
2.
(a)
(2)
An unbiased point estimate of
, the average amount of gas used by all houses in the area is:
therms
x
6
.
120
10
206
,
1
(b)
(2)
An unbiased point estimate of
, the proportion of all homes that use over 100 therms is:
80
.
10
8
p
6.
(a)
(3)
An unbiased point estimate of
, the average number of flaws on a randomly chosen item is:
11
.
2
150
317
ˆ
(b)
(2)
The standard error of
ˆ
is:
8.
(a)
(1)
98% of the standard normal curve area must be captured.
This requires that 1% of the area is to be
captured in each tail of the distribution.
So, P(Z < z critical value) = .01 and P(Z > z critical value) = .01.
Thus,
the z critical value = 2.33.
(b)
(1)
85% of the standard normal curve area must be captured.
This requires that 7.5% of the area is to be
captured in each tail of the distribution.
So, P(Z < z critical value) = .075 and P(Z > z critical value) = .075.
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 Spring '08
 Staff
 Statistics, Normal Distribution, critical value, standard normal curve, twosided confidence interval, normal curve area

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