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7.8 Review

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

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

  • f ( x ) = 1 10 size 12{f \( x \) = { {1} over {"10"} } } {} , 3 ≤ x ≤ 13 size 12{3<= x<= "13"} {}
  • There is no mode.
  • The median is less than the mean.
  • P ( X > 10 ) = P ( X ≤ 6 ) size 12{P \( X>"10" \) =P \( X<= 6 \) } {}
  • True
  • True
  • False – the median and the mean are the same for this symmetric distribution
  • True

Calculate:

  • Mean
  • Median
  • 65th percentile.
Horizontal boxplot with first whisker at 0 to 2, box from 2 to 5, line at 4, and second whisker from 5 to 7.
  • 8
  • 8
  • P ( X < k ) = 0 . 65 = ( k − 3 ) ∗ ( 1 10 ) size 12{P \( X<k \) =0 "." "65"= \( k - 3 \) * \( { {1} over {"10"} } \) } {} . k = 9 . 5 size 12{k=9 "." 5} {}

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

  • 25% of the data are at most 5.
  • There is about the same amount of data from 4 – 5 as there is from 5 – 7.
  • There are no data values of 3.
  • 50% of the data are 4.
  • False – 3 4 size 12{ { {3} over {4} } } {} of the data are at most 5
  • True – each quartile has 25% of the data
  • False – that is unknown
  • False – 50% of the data are 4 or less

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

  • G size 12{G} {} and H size 12{H} {} are mutually exclusive events.
  • P ( G ) = P ( H ) size 12{P \( G \) =P \( H \) } {}
  • Knowing that H size 12{H} {} has occurred will affect the chance that G size 12{G} {} will happen.
  • G size 12{G} {} and H size 12{H} {} are independent events.

D

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

  • P ( J and K ) = 0
  • P ( J or K ) = 0.9
  • P ( J or K ) = 0.72
  • P ( J ) ≠ P ( J ∣ K )
  • False - J and K are independent so they are not mutually exclusive which would imply dependency (meaning P(J and K) is not 0).
  • False - see answer C.
  • True - P(J or K) = P(J) + P(K) - P(J and K) = P(J) + P(K) - P(J)P(K)= 0.3 + 0.6 - (0.3)(0.6) = 0.72. Note that P(J and K) = P(J)P(K) because J and K are independent.
  • False - J and K are independent so P(J) = P(J|K).
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Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
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