Chapter 6
6 - 4
e.
P
(
x
≥
290)
=
.0386(310.6 - 290) = .7952
6.
a.
P
(12
≤
x
≤
12.05)
=
.05(8)
=
.40
b.
P
(
x
≥
12.02)
=
.08(8)
=
.64
c.
(
11.98)
(
12.02)
.005(8)
.04
.64
.08(8)
P x
P x
<
+
>
=
=
±²²³²²´
±²²³²²´
Therefore, the probability is .04 + .64
=
.68
7.
a.
P
(10,000
≤
x
<
12,000)
=
2000 (1 / 5000)
=
.40
The probability your competitor will bid lower than you, and you get the bid, is .40.
b.
P
(10,000
≤
x
<
14,000)
=
4000 (1 / 5000)
=
.80
c.
A bid of $15,000 gives a probability of 1 of getting the property.
d.
Yes, the bid that maximizes expected profit is $13,000.
The probability of getting the property with a bid of $13,000 is
P
(10,000
≤
x
<
13,000)
=
3000 (1 / 5000)
=
.60.
The probability of not getting the property with a bid of $13,000 is .40.
The profit you will make if you get the property with a bid of $13,000 is $3000
=
$16,000 -
13,000.
So your expected profit with a bid of $13,000 is
EP ($13,000)
=
.6 ($3000) + .4 (0)
=
$1800.
If you bid $15,000 the probability of getting the bid is 1, but the profit if you do get the bid is only
$1000
=
$16,000 - 15,000.
So your expected profit with a bid of $15,000 is
EP ($15,000)
=
1 ($1000) + 0 (0)
=
$1,000.
8.
100
= 10
σ
70
80
90
110
120
130