IDS 301
Part 1
Chapters 3 through 9
1.
You receive 18 pieces of mail a week.
The amount of mail you receive each week is
independent of each other and does not influence how much you may receive the next week.
There
is no mail on Sundays.
What is the expected number of pieces of mail you will get in a day?
3
6
18
÷
What is the probability that you receive more than 1 piece of mail in a given day?
.80085
[
]
)
1
(
)
0
(
1
)
1
(
P
P
x
P
+

=
P(0)=.04979
P(1)=.14936
2.
The unemployment rate in San Diego is 6.2%.
What is the probability that you select 100 people and at most 3 are unemployed? .1261
)
3
(
)
2
(
)
1
(
)
0
(
)
3
(
P
P
P
P
x
P
+
+
+
=
≤
P(0)=.00166
P(1)=.01098
P(2)=.03591
P(3)=.07755
If you pick 100 people, what is the expected number of people that will be unemployed?
6.2
n x p = 100 x .062
What is the probability that at least 2 of the 100 people are unemployed?
.98736
[
]
)
1
(
)
0
(
1
)
2
(
P
P
x
P
+

=
≥
3.
The average number of minutes a person uses their cell phone is 1,548 minutes per month
with a standard deviation of 378 minutes.
If you randomly select 50 people, what is the probability
that they use their phone for more than 1,650 minutes?
0281
.
)
91
.
1
(
)
1650
(
=
=
Z
P
x
P
What is the probability that they use their phone less than 1575 minutes per month?
6950
.
)
51
.
(
)
1575
(
=
<
=
<
Z
P
x
P
What is the probability that they use their phone less than 1500 minutes per month?
1841
.
)
90
.
(
)
1500
(
=

<
=
<
Z
P
x
P
What is the probability that they use their phone between 1400 minutes and 1600 minutes per
month?
8312
.
0028
.
8340
.
)
97
.
77
.
2
(
)
1600
1400
(
=

=
<
<

=
<
<
Z
P
x
P
If the population was normally distributed, what is the probability that you select 1 person and they
use their cell phone for more than 2,000 minutes?
1151
.
)
20
.
1
(
)
2000
(
=
=
Z
P
x
P
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If the population was normally distributed, what is the probability that you select 1 person and they
use their cell phone for less than 750 minutes?
0174
.
)
11
.
2
(
)
750
(
=

<
=
<
Z
P
x
P
If the population was normally distributed, what is the probability that you select 1 person and they
use their cell phone between 1200 and 2300 minutes per month?
7979
.
1788
.
9767
.
)
99
.
1
92
.
(
)
2300
1200
(
=

=
<
<

=
<
<
Z
P
x
P
Where does the top 3% of users start?
2258.64
Z=1.88
4.
The Cable Guy arrives for his appointment in a five hour window.
His arrival times are
uniformly distributed.
If you have an appointment with the cable guy and his 5 hour window is from 8
AM to 1 PM, what is the probability that he will show up after 9 AM?
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 Spring '08
 shaul
 Probability, Standard Deviation, San Diego

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