# stats homework 5 assignments

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

^3 instead of 8, sin(3 pi=2)instead of -1, e ^(ln(2)) instead of 2, (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

answer:

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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

answer:

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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?

Answer:

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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)

.gif”>w = 3x + 1

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.

answer:

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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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Answer(s) submitted:

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?

answer:

(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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Answer(s) submitted:

(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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