Passengers using New York\'s MetroCard system must swipe the card at a rate betw

Question

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 the following: (Round your answers to 2 decimal places.)

(a) Mean swipe rate
(b) Standard deviation of the swipe rate
(c-1) 1st Quartile
(c-2) 3rd Quartile

(d)
What percentage of subway riders must re-swipe the card because they were outside the acceptable range? (Round your answer to 4 decimal places. Omit the "%" sign in your response.)

Percentage of subway riders who must re-swipe %

Explanation / Answer

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. --- Draw a picture of the uniform distribution. Base has width 50-5 = 45 Therefore height = 1/45 ------------------------------- 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 --------------------------------------------- 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 ------------------------------- 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 ------------------------------- e. what percentage of subway riders must re-swipe the card because they were outside the acceptable range? Ans: 1 - P(10

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