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Midterm Review – Normal and Sampling Distributions
1. Normal distribution (section 53)
Researchers studying the effects of a new diet found that the weight loss over a one
month period by those on the diet was normally distributed with a mean of 3 kilograms
and a standard deviation of 1 kilogram.
Answers
(a)
What proportion of the dieters lost more than 4 kilograms? (1 mark)
(b)
What proportion of the dieters gained weight? (1 mark)
(c)
If a dieter is selected at random, what is the probability that the dieter lost
at most 2.5 kilograms? (1 mark)
Note that we are not speaking about a sample of dieters anywhere in this question. This
is a plain normal distribution question.
(a)
1587
.
0
3413
.
0
1
)
1
Z
0
(
P
1
)
1
Z
(
P
1
3
4
X
P
)
4
X
(
P
=

=
<
<

=
=

σ
μ

=
(b) Gaining weight means having a negative weight loss:
0013
.
0
4987
.
0
1
)
0
Z
3
(
P
1
)
3
Z
(
P
1
3
0
X
P
)
0
X
(
P
=

=
<
<


=

<
=

<
σ
μ

=
<
(c)
3085
.
0
1915
.
0
1
)
0
Z
5
.
0
(
P
1
)
5
.
0
Z
(
P
1
3
5
.
2
X
P
)
5
.
2
X
(
P
=

=
<
<


=

<
=

<
σ
μ

=
<
2. Normal distribution, sampling distribution for means (section 62) and the rules
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This note was uploaded on 09/25/2010 for the course OMIS OMIS 1000 taught by Professor Alexandershoumarov during the Fall '09 term at York University.
 Fall '09
 ALEXANDERSHOUMAROV

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