Passengers using New York\'s MetroCard system must swipe the card at a rate betw
ID: 2784330 • Letter: P
Question
Passengers using New York's MetroCard system must swipe the card at a rate between 10 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 2 and 41 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 %
Explanation / Answer
(a) What is the mean swipe rate?
Mean swipe rate=(41-2)/2=39/2=19.5
(b) standard deviation of the swipe rate
= sqrt[[(41-2)+1]2-1] /12]= sqrt[[402-1] /12] = 11.54
(c) What are the quartiles
here 25th percentile =1st quartile =2+0.25*(41-2)=11.75
and 3rd quartile =75th percentile =2+0.75*(41-2)=31.25
(d) What percentage of subway riders must re-swipe the card because they were outside the acceptable range?
From above calculation the percentage of subway riders must re-swipe the card because they were outside the acceptable range
=(((10-2)+(41-36))/(41-2))*100 =(13/39)*100 =33.33%
Note- Kindly give a thumbs up if you are satisfied with the answer. Would help me a lot. Thanks.