THE UNIVERSITY OF SYDNEY
Math1005 Statistics
Semester 2
Tutorial Week 8
2006
We encourage you to attempt these problems before your tutorial class.
1. Multiple choice
X
is binomial with
n
= 100 and
p
= 0
.
4 Which of the following
normal distributions is a good approximation to the distribution of
X
?
(a)
N
(100
,
0
.
4).
(b)
N
(40
,
24).
(c)
N
(100
,
0
.
16).
(d) standard normal.
(e)
N
(
40
,
24
100
)
.
2. Multiple choice
P
(
X
≤
38) in Q1 (using the normal approximation with continuity
correction) is:
3.
The proportion of families buying orange juice from JUJUJUICE of Australia in a certain
city is believed to be 0.6. A consumer group claims that JUJUJUICE is now less popular
than it was before. A random sample of 50 families from this city shows that only 22 buy
JUJUJUICE. Let
p
be the probability of consumption of JUJUJUICE.
(a) Explain why a onesided test of
H
0
:
p
= 0
.
6
vs.
H
1
:
p <
0
.
6 is suitable to test the
claim of this consumer group
(b) Let
X
be the number of families in the sample of 50 who consume JUJUJUICE.
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 Normal Distribution, Variance, Probability theory, Binomial distribution, JUJUJUICE

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