Practice Midterm Exam 1 - Economics 120a, Fall 2009
1. Examine the following histogram.
0
0
1
2
3
4
5
6
7
8
9
10
5
10
15
20
25
30
(a) What do you think the mean and median are roughly.
The mode is clearly 6.
There seems to be little deviation from symmetry – maybe a little skewness to the
left.
Hence we would expect the median and the mean to be somewhere near 6, maybe a little lower.
We
could try and count the number of observations in each column to work out the median directly, but we
would still come to the conclusion that it is in the range of between 5 and 6.
This is a non-tricky problem –
often when there is enough data distributions tend towards the symmetric and there is little difference
between the measures of central tendency.
(b) Is either better than the other?
Since they are all the same there is little argument as to which is best.
2. In general, 40% of the customers in a certain store pay with a credit card.
a) What is the chance that 8 of the 11 customers in a day pay with cash?
If we think of a ‘success’ as cash payment then
π
=P[cash payment] = 0.6.
Using the binomial model with
n=11 we want P[S=8|11]
= 17.7%
from our tables.
b) What is the chance that less than three of 11 customers pay with a credit card?
We have defined S as number paying with cash so the chance that less than three pay with the credit card is
chance that more than 8 pay with cash.
P[S>8|11] = P[S
≥
9|11] =
11.9% from our tables
3. Question
4-20, 4-22 pp 133-134, 4-36, p147.
Answer 4-20.
a)
P X
P
X
P Z
(
)
(
. )
. .
>
=
−
>
−
⎛
⎝
⎜
⎞
⎠
⎟ =
>
=
20
16
5
20
16
5
08
0 212
b)

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