Question

Passengers using New York's MetroCard system must swipe the card at a rate between 8 and 36 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 3 and 45 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             inches per second

(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.)
  
Re-swipe             %

Answer 1

Let x be the swipe rates inches per second.

x follows uniform distribution with constants a = 3 and b = 45

Distribution function of x is given by ,

P( X ≤ x ) = =

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

= 24 inches per second

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

= 12.12 inches per second

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

The area less than 1st quartile is 0.25 , so by using distribution function formula

0.25 =  

Q1 = ( 0.25*42 ) + 3

Q1 = 13.5

The area less than 3rd quartile is 0.75 , so by using distribution function formula

0.75 =  

Q1 = ( 0.75*42 ) + 3

Q1 = 34.5

1st Quartile	13.5 inches per second
3rd Quartile	34.5 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.)

Acceptable range is between 8 and 36 inches per second

P( 8 ≤ x ≤ 36 ) = P( x ≤36 ) - P( x ≤ 8 )

=    

= 0.7857 - 0.1190

=0.6667 or 66.67%

So % outside the acceptable range is 100% - 66.67% = 33.33%

Re-swipe 33.33 %