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Central Limit Theorem: Review

Module by: Dr. Barbara Illowsky, Susan Dean

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 \( 2,1 \) } {}

Solution 1

A

Exercise 2

The average wait time is:

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

Solution 2

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} } } {}

Solution 3

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 \( X= { {1} over {3} } \) } {}

Solution 4

  • 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

Solution 5

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

Solution 6

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

Solution 7

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" \( { {1} over {0 "." "20"} } \) } {}

Solution 8

A

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