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 14 and 34 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 40 inches per second.

(a) What is the mean swipe rate? (Round your answer to 2 decimal places.) Mean inches per second

(b) What is the standard deviation of the swipe rate? (Round your answer to 2 decimal places.)

(c) What are the quartiles? (Round your answers to 2 decimal places.)

1st Quartile inches per second

3rd Quartile inches per second

(d) What percentage of subway riders must re-swipe the card because they were outside the acceptable range? (Round your answer to 2 decimal places.)

Chapter Exercise 7-68 Passengers using New York's MetroCard system must swipe the card at a rate between 14 and 34 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 40 inches per second. (a) What is the mean swipe rate? (Round your answer to 2 decimal places.) Mean inches per second b) What is the standard deviation of the swipe rate? (Round your answer to 2 decimal places.) Standard deviation 10.10 inches per second (c) What are the quartiles? (Round your answers to 2 decimal places.) 1st Quartile 3rd Quartile inches per second inches per second (d) What percentage of subway riders must re-swipe the card because they were outside the acceptable range? (Round your answer to 2 decimal places.) Re-swipe

Explanation / Answer

a) from unform distribution mean swipe rate =(5+40)/2 =22.5

b) standard deviation of the swipe rate =(40-5)/(12)1/2 = 10.10

c)1st Quartile =5+0.25*(40-5)=13.75

3rd quartile =5+0.75*(40-5)=31.25

d)percentage of subway riders must re-swipe the card because they were outside the acceptable range

=P(X<14 )+P(X>34)=(14-5)/35+(40-34)/35=0.4286 ~42.86%

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