SOLUTION: passengers using new york's metrocard system must swipe the card at a rate between 10 and 40 inches per second, or else the card must be re-swiped through the card reader. Research

Question 285982: passengers using new york's metrocard system must swipe the card at a rate between 10 and 40 inches per second, or else the card must be re-swiped through the card reader. Research shows that actual swipe rates by subway riders are uniformly distributed between 5 and 50 inches per second.
Determine:
a. mean swipe rate - i got 27.5
b. standard deviation of the swipe rate - i got 12.99
c. 1st quartile
d. third quartile
e. what percentage of subway riders must re-swipe the card because they were outside the acceptable range?

Not sure about quartiles and e., and hope a. and b. are correct
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
passengers using new york's metrocard system must swipe the card at a rate between 10 and 40 inches per second, or else the card must be re-swiped through the card reader.
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Draw a picture of the uniform distribution.
Base has width 50-5 = 45
Therefore height = 1/45
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Research shows that actual swipe rates by subway riders are uniformly distributed between 5 and 50 inches per second.

Determine:
a. mean swipe rate - (50-5)/2 = 27.5
--------------------------------------------
b. standard deviation of the swipe rate - i got 12.99
Note: I'm not sure how you got 12.99.
The formula I find is sqrt[[(50-5)+1]^2 -1]/12] = sqrt[[46^2-1]/12] = 13.28
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c. 1st quartile
Point with left tail = 0.25
base(1/45) = 0.25
base = 45*0.25
base = 11.25
But base starts at 5 so the 1st quartile value is 5+11.25 = 16.25
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d. third quartile
Point with left tail of 0.75
base(1/45) = 0.75
base = 45*0.75
base = 33.75
But base starts at 5 so the 3rd quartile value is 5+33.75 = 38.75
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e. what percentage of subway riders must re-swipe the card because they were outside the acceptable range?
Ans: 1 - P(10<= x <=40) = 1 - (30/45) = 1 - 2/3 = 1/3 = 33.33%

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Cheers,
Stan H.

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