Passengers using New York\'s MetroCard system must swipe the card at a rate betw
ID: 3359117 • Letter: P
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 6 and 46 inches per second.
What is the mean swipe rate? (Round your answer to 2 decimal places.)
What is the standard deviation of the swipe rate? (Round your answer to 2 decimal places.)
What are the quartiles? (Round your answers to 2 decimal places.)
What percentage of subway riders must re-swipe the card because they were outside the acceptable range? (Round your answer to 2 decimal places.)
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 6 and 46 inches per second.
Explanation / Answer
a. mean swipe rate - (46 - 6)/2 = 20
b) SD = (46 - 6)/12 = 11.55
c)
Base has width 46 - 6 = 40
Therefore height = 1/40
1st quartile
Point with left tail = 0.25
base(1/40) = 0.25
base = 40 * 0.25
base = 10
But base starts at 6 so the 1st quartile value is 6 + 10 = 16
third quartile
Point with left tail of 0.75
base(1/40) = 0.75
base = 40*0.75
base = 30
But base starts at 6 so the 3rd quartile value is 6+30 = 36
d) 1 - P(10<= x <=40) = 1 - (30/40) = 1 - 3/4 = 1/4 = 25%