# stats homework 5 assignments

| October 3, 2018

Homework 5Summer is
due on Monday, June 08, 2015 at 11:58pm.
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The number of attempts available for each
question is noted beside the question. If you are having trouble figuring out
your error, you should consult the textbook, or ask a fellow student, one of
the TA’s or your professor for help.

There
are also other resources at your disposal, such as the Engineering Drop in
Centre and the Mathematics Continuous Tutorials. Don’t spend a lot of time
guessing – it’s not very efficient or effective.

Make sure to give lots of significant digits
for (floating point) numerical answers. For most problems when entering
numerical answers, you can if you wish enter elementary expressions such as 2
tan(3)) (4 sin(5)) ^6 7=8 instead of 27620.3413, etc.
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1.
(1 point) Recent statistics have indicated that of all trafficc fatalities from
single-vehicle accidents: 58 (a) was the occupant of an SUV and not wearing a
seatbeat?
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(b) was the
occupant of an SUV or not wearing a seatbeat?

(c)was wearing
a seatbelt or not an occupant of an SUV?

(d)
It was determined that the
person involved in this accident was wearing a seatbeat. What is the
probability this person was an occupant of an SUV?

(e)
True or False: The events
the victim of a single-vehicle traffic fatality was not wearing a seatbeat and
the victim of
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a single-vehicle traffic fatality was an
occupant of an SUV are independent events. (Y/N) Justify your answer with
prob-ability theory. A failure to do so will earn you zero marks.
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2. (2
points) A bank has studied its chequing accounts and found that 98% of all
chequing accounts have been open for at least one year, the remaining
percentage of chequing accounts have been open for less than a year. The bank
also determined that for all chequing accounts that have been open for less
than one year, the percentage of cheques returned due to insufficient funds is
5%. For chequing accounts that have been open for at least one year, only 1% of
cheques were returned due to insuffi-cient funds.

(a)
What is the probability that a cheque processed by this bank will be returned
due to insufficient funds?
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(b) If a cheque is returned
due to insufficient funds, what is the probability that it came from a bank
account that has been open for more than one year?
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3. (3
points) Determine whether the following are valid prob-ability distributions or
not. Type ”VALID” if it is valid, or type ”INVALID” if it is not a valid
probability distributions.

(a)

x

1

2

3

5

P(x)

0:5

0:1

0:2

0:2

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(b)

P(x)
=21x
, where x = 1; 2; 3;::: answer:
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(c)

x

1

2

3

5

P(x)

0

0:2

0:2

1

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4. (1
point) Of 310 male and 290 female employees at the Flagstaff Mall, 200 of the
men and 210 of the women are on flex-time (flexible working hours). Given that
an employee se-lected at random from this group is on flex-time, what is the
probability that the employee is a woman?

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5. (6
points) The mean and standard deviation of a random variable x are 4 and 2
respectively. Find the mean and standard deviation of the given random
variables:

(1)
y = x + 1

µ=
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s =

(2)
v = 3x

µ =

s =
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1

(3)
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µ=
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s =
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6.
(1 point) Factories A and B produce computers. Factory A produces 4 times as
many computers as factory B. The probabil-ity that an item produced by factory
A is defective is 0.027 and the probability that an item produced by factory B
is defective is 0.038.

A computer is selected at
random and it is found to be defective. What is the probability it came from
factory A?

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7. (4
points) Three Toronto Maple Leaf fans attend a Flames-Leafs game in the
Saddledome. The probability that the first fan will wear their ”Leafs” jersey
is 0.87. The probability that the second fan will wear their ”Leafs” jersey is
0.88. The probabil-ity that the third fan will not wear their ”Leafs” jersey is
0.51. Let X be a random variable which measures how many of the three Leaf fans
mentioned are wearing their ”Leafs” jersey to this hockey game.

Assuming
that each ”Leaf” fan mentioned wears their ”Leaf” jersey independently of each
other,find the probability distribu-tion of X.

P(X = 0) =
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P(X = 1) =
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P(X = 2) =
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P(X = 3) =
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8. (1 point)

”Channel One” is an educational
television network for which participating secondary schools are equipped with
TV sets in ev-ery classroom. It has been found that 55% of secondary schools
subscribe to Channel One, where of these subscribers 5% never

use Channel One while 35%
claim to use it more than 5 times per week.

Find
the probability that a randomly selected seconday school subscribes to Channel
One and uses it more than 5 times per week.

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9. (5 points) Based on recent records,
the manager of a car painting center has determined the following probability
distri-bution for the number of customers per day.

x

0

1

2

3

4

5

f(x)

0.05

0.16

0.25

0.23

0.1

0.21

If the center has the
capacity to serve two customers per day,

(a)
what is the probability that
one or more customers will be turned away on a given day ?

(b)
what is the probability that
the center’s capacity will not be fully utilized on a day ?
(c)
by how much must the
capacity be increased so the proba-bility of turning a customer away is less
than 0.10 ?

(d)Find the
mean and standard deviation of X.
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µ
= s =
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0.54 0.21

4

2.8
1.496662955

(score
0.800000011920929)
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10.
(2 points) Scoring a hole-in-one is the greatest shot a golfer can make. Once 3
professional golfers each made holes-in-one on the 7th
hole at the same golf course at the same tourna-ment. It has been found that
the estimated probability of making

a hole-in-one is22101
for male professionals. Suppose that a sam-ple of 3 professional male golfers
is randomly selected.
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(a)
What is the approximate
probability that all of these golfers make a hole-in-one on the 16th
hole at the same tour-nament?

(b)
What is the probability that
at least one of these golfers makes a hole-in-one on the 16th
hole at the same tournament?
2

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(2 points) A manufacturer produces 3 lines of jackets. Records indicate that 42
% of the jackets are priced at \$ 150 (Line A), 33 % are priced at \$ 200 (Line
B) and 25 % are priced at \$ 250. Let X be the random variable representing the
price of a jacket.
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E(X) = V (X) =
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(incorrect)

12.
(1 point) There are four activities along the critical path for a project. The
expected values and variances of the comple-tion times of the activities are
listed below. Determine the ex-pected value and variance of the completion time
of the project.
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Generated by c
WeBWorK, http://webwork.maa.org, Mathematical Association of America

Activity

Expected
Completion Time (Days)

Variance

1

16

6

2

10

5

3

24

6

4

6

2

Expected
value of completion time of project = Variance of completion time of project =

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