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Central Limit Theorem: Review (modified R. Bloom)

Module by: Roberta Bloom. E-mail the author

Based on: Central Limit Theorem: Review by Susan Dean, Barbara Illowsky, Ph.D.

Summary: Practice problems in elementary statistics. One problem in the original module by S. Dean and Dr. B. Illowsky has been revised.

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: REVIEW QUESTION 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 \( 2,1 \) } {}

Solution

REVIEW QUESTION 1 Solution : A

Exercise 2: REVIEW QUESTION 2

The average wait time is:

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

Solution

REVIEW QUESTION 1 Solution : B

Exercise 3: REVIEW QUESTION 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} } } {}

Solution

REVIEW QUESTION 3 Solution : A

Exercise 4: REVIEW QUESTION 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 \( X= { {1} over {3} } \) } {}

Solution

REVIEW QUESTION 4 Solution

  • a. 0.7165
  • b. 4.16
  • c. 0

Exercise 5: REVIEW QUESTION 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

Solution

REVIEW QUESTION 5 Solution : C

Exercise 6: REVIEW QUESTION 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

Solution

REVIEW QUESTION 6 Solution : C

Exercise 7: REVIEW QUESTION 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

Solution

REVIEW QUESTION 7 Solution : D

Exercise 8: REVIEW QUESTION 8

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

REVIEW QUESTION 8 Solution : A

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