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# Central Limit Theorem: Review

Summary: Central Limit Theorem: Review is part of the collection col10555 written by Barbara Illowsky and Susan Dean. The module consists of review exercises.

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The next three questions refer to the following information: Richard’s Furniture Company delivers furniture from 10 A.M. to 2 P.M. continuously and uniformly. We are interested in how long (in hours) past the 10 A.M. start time that individuals wait for their delivery.

## Exercise 1

X X size 12{X "~" } {} ~

• A. U ( 0,4 ) U ( 0,4 ) size 12{U $$0,4$$ } {}
• B. U ( 10 , 2 ) U ( 10 , 2 ) size 12{U $$"10",2$$ } {}
• C. Exp ( 2 ) Exp ( 2 ) size 12{ ital "Exp" $$2$$ } {}
• D. N ( 2,1 ) N ( 2,1 ) size 12{N $$2,1$$ } {}

A

## Exercise 2

The average wait time is:

• A. 1 hour
• B. 2 hour
• C. 2.5 hour
• D. 4 hour

B

## Exercise 3

Suppose that it is now past noon on a delivery day. The probability that a person must wait at least 1 1 2 1 1 2 size 12{1 { {1} over {2} } } {} more hours is:

• A. 1 4 1 4 size 12{ { {1} over {4} } } {}
• B. 1 2 1 2 size 12{ { {1} over {2} } } {}
• C. 3 4 3 4 size 12{ { {3} over {4} } } {}
• D. 3 8 3 8 size 12{ { {3} over {8} } } {}

A

## Exercise 4

Given: X~Exp(13)X~Exp(13) size 12{X "~" ital "Exp" $${ {1} over {3} }$$ } {}.

• a. Find P(x>1)P(x>1) size 12{P $$x>1$$ } {}
• b. Calculate the minimum value for the upper quartile.
• c. Find P(x=13)P(x=13) size 12{P $$x= { {1} over {3} }$$ } {}

• a. 0.7165
• b. 4.16
• c. 0

## Exercise 5

• 40% of full-time students took 4 years to graduate
• 30% of full-time students took 5 years to graduate
• 20% of full-time students took 6 years to graduate
• 10% of full-time students took 7 years to graduate

The expected time for full-time students to graduate is:

• A. 4 years
• B. 4.5 years
• C. 5 years
• D. 5.5 years

C

## Exercise 6

Which of the following distributions is described by the following example?

Many people can run a short distance of under 2 miles, but as the distance increases, fewer people can run that far.

• A. Binomial
• B. Uniform
• C. Exponential
• D. Normal

C

## Exercise 7

The length of time to brush one’s teeth is generally thought to be exponentially distributed with a mean of 3 4 3 4 size 12{ { {3} over {4} } } {} minutes. Find the probability that a randomly selected person brushes his/her teeth less than 3 4 3 4 size 12{ { {3} over {4} } } {} minutes.

• A. 0.5
• B. 3 4 3 4 size 12{ { {3} over {4} } } {}
• C. 0.43
• D. 0.63

D

## Exercise 8

Which distribution accurately describes the following situation?

The chance that a teenage boy regularly gives his mother a kiss goodnight (and he should!!) is about 20%. Fourteen teenage boys are randomly surveyed.

X=X= size 12{X={}} {}the number of teenage boys that regularly give their mother a kiss goodnight

• A. B ( 14 , 0 . 20 ) B ( 14 , 0 . 20 ) size 12{B $$"14",0 "." "20"$$ } {}
• B. P ( 2 . 8 ) P ( 2 . 8 ) size 12{P $$2 "." 8$$ } {}
• C. N ( 2 . 8,2 . 24 ) N ( 2 . 8,2 . 24 ) size 12{N $$2 "." 8,2 "." "24"$$ } {}
• D. Exp ( 1 0 . 20 ) Exp ( 1 0 . 20 ) size 12{ ital "Exp" $${ {1} over {0 "." "20"} }$$ } {}

A

## Exercise 9

Which distribution accurately describes the following situation?

A 2008 report on technology use states that approximately 20 percent of U.S. households have never sent an e-mail. (source: http://www.webguild.org/2008/05/20-percent-of-americans-have-never-used-email.php) Suppose that we select a random sample of fourteen U.S. households .

X=X= size 12{X={}} {}the number of households in the sample of 14 households that have never sent an email

• A. B ( 14 , 0 . 20 ) B ( 14 , 0 . 20 ) size 12{B $$"14",0 "." "20"$$ } {}
• B. P ( 2 . 8 ) P ( 2 . 8 ) size 12{P $$2 "." 8$$ } {}
• C. N ( 2 . 8,2 . 24 ) N ( 2 . 8,2 . 24 ) size 12{N $$2 "." 8,2 "." "24"$$ } {}
• D. Exp ( 1 0 . 20 ) Exp ( 1 0 . 20 ) size 12{ ital "Exp" $${ {1} over {0 "." "20"} }$$ } {}

### Solution

A

**Exercise 9 contributed by Roberta Bloom

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