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

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.

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

  • U ( 0,4 ) size 12{U \( 0,4 \) } {}
  • U ( 10 , 2 ) size 12{U \( "10",2 \) } {}
  • Exp ( 2 ) size 12{ ital "Exp" \( 2 \) } {}
  • N ( 2,1 ) size 12{N \( 2,1 \) } {}

A

The average wait time is:

  • 1 hour
  • 2 hour
  • 2.5 hour
  • 4 hour

B

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

  • 1 4 size 12{ { {1} over {4} } } {}
  • 1 2 size 12{ { {1} over {2} } } {}
  • 3 4 size 12{ { {3} over {4} } } {}
  • 3 8 size 12{ { {3} over {8} } } {}

A

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

  • Find P ( x > 1 ) size 12{P \( x>1 \) } {}
  • Calculate the minimum value for the upper quartile.
  • Find P ( x = 1 3 ) size 12{P \( x= { {1} over {3} } \) } {}
  • 0.7165
  • 4.16
  • 0
  • 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:

  • 4 years
  • 4.5 years
  • 5 years
  • 5.5 years

C

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.

  • Binomial
  • Uniform
  • Exponential
  • Normal

C

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

  • 0.5
  • 3 4 size 12{ { {3} over {4} } } {}
  • 0.43
  • 0.63

D

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

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

A

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 = size 12{X={}} {} the number of households in a 2008 sample of 14 households that have never sent an email

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

A

**Exercise 9 contributed by Roberta Bloom

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Source:  OpenStax, Collaborative statistics (custom lecture version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11543/1.1
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