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Textbook by: Vicky Moyle. E-mail the author

Review Questions

Module by: Roberta Bloom. E-mail the author

Summary: Copy of Review Questions module m16985 (http://cnx.org/content/m16985/) from Collaborative Statistics by Dean and Illowsky http://cnx.org/content/col10522/ , 12/18/2008 . The FORMAT only of the question numbering has been changed.

The next two questions refer to: X X ~ U ( 3 , 13 ) U(3,13)

Exercise 1: REVIEW QUESTION 1

Explain which of the following are false and which are true.

• a: f(x)=110f(x)=110 size 12{f $$x$$ = { {1} over {"10"} } } {}, 3x133x13 size 12{3 <= x <= "13"} {}
• b: There is no mode.
• c: The median is less than the mean.
• d: P ( X > 10 ) = P ( X 6 ) P ( X > 10 ) = P ( X 6 ) size 12{P $$X>"10"$$ =P $$X <= 6$$ } {}

Solution

REVIEW QUESTION 1 Solution

• a: True
• b: True
• c: False – the median and the mean are the same for this symmetric distribution
• d: True

Exercise 2: REVIEW QUESTION 2

Calculate:

• a: Mean
• b: Median
• c: 65th percentile.

Solution

REVIEW QUESTION 2 Solution

• a: 8
• b: 8
• c: P(X<k)=0.65=(k3)(110)P(X<k)=0.65=(k3)(110) size 12{P $$X<k$$ =0 "." "65"= $$k - 3$$ * $${ {1} over {"10"} }$$ } {}. k=9.5k=9.5 size 12{k=9 "." 5} {}

Exercise 3: REVIEW QUESTION 3

Which of the following is true for the above box plot?

• a: 25% of the data are at most 5.
• b: There is about the same amount of data from 4 – 5 as there is from 5 – 7.
• c: There are no data values of 3.
• d: 50% of the data are 4.

Solution

REVIEW QUESTION 3 Solution

• a: False – 3434 size 12{ { {3} over {4} } } {} of the data are at most 5
• b: True – each quartile has 25% of the data
• c: False – that is unknown
• d: False – 50% of the data are 4 or less

Exercise 4: REVIEW QUESTION 4

If P(GH)=P(G)P(GH)=P(G) size 12{P $$G \lline H$$ =P $$G$$ } {}, then which of the following is correct?

• A: GG size 12{G} {} and HH size 12{H} {} are mutually exclusive events.
• B: P ( G ) = P ( H ) P ( G ) = P ( H ) size 12{P $$G$$ =P $$H$$ } {}
• C: Knowing that HH size 12{H} {} has occurred will affect the chance that GG size 12{G} {} will happen.
• D: GG size 12{G} {} and HH size 12{H} {} are independent events.

D

Exercise 5: REVIEW QUESTION 5

If P(J)=0.3P(J)=0.3 size 12{P $$J$$ =0 "." 3} {}, P(K)=0.6P(K)=0.6 size 12{P $$K$$ =0 "." 6} {}, and JJ size 12{J} {} and KK size 12{K} {} are independent events, then explain which are correct and which are incorrect.

• A: P(JP(J size 12{P $$J} {} and K)=0K)=0 size 12{K$$ =0} {}
• B: P(JP(J size 12{P $$J} {} or K)=0.9K)=0.9 size 12{K$$ =0 "." 9} {}
• C: P(JP(J size 12{P $$J} {} or K)=0.72K)=0.72 size 12{K$$ =0 "." "72"} {}
• D: P ( J ) P ( J K ) P ( J ) P ( J K ) size 12{P $$J$$ <> P $$J \lline K$$ } {}

Solution

REVIEW QUESTION 5 Solution

• A: False – JJ size 12{J} {} and KK size 12{K} {} are independent, so they are not mutually exclusive which would imply dependency
• B: False
• C: True – since P(JP(J size 12{P $$J} {} and K)0K)0 size 12{K$$ <> 0} {}, then P(JP(J size 12{P $$J} {} or K)<0.09K)<0.09 size 12{K$$ <0 "." "09"} {}
• D: False – P(JP(J size 12{P $$J} {} and K)0K)0 size 12{K$$ <> 0} {} are independent which implies P(J)=P(JK)P(J)=P(JK) size 12{P $$J$$ =P $$J \lline K$$ } {}

Exercise 6: REVIEW QUESTION 6

On average, 5 students from each high school class get full scholarships to 4-year colleges. Assume that most high school classes have about 500 students.

XX = the number of students from a high school class that get full scholarships to 4-year school. Which of the following is the distribution of XX?

• A. P(5)
• B. B(500,5)
• C. Exp(1/5)
• D. N(5, (0.01)(0.99)/500)

A

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