Answer:
E(X) = 27.5 in/s
s.d (X) = 13.28 in/s
1st quartile = 16.25 in/s
3rd quartile = 38.75 in/s
33.33%
Step-by-step explanation:
Solution:-
- The Research shows that actual swipe rates by subway riders are uniformly distributed between 5 and 50 inches per second.
- The uniform distribution of the swipe rate can be expressed by the limits of swipe rates as [ a , b ] as follows:
- The random variable X follows a uniform distribution for the rate of card swiped expressed by parameters [ 5 , 50 ].
X ~ U ( 5 , 50 )
a) The mean value E(X) for the distribution is:
E(X) = ( b - a ) / 2
E(X) = (50-5) / 2
E(X) = 27.5 in/s
b) The standard deviation s.d for the distribution is as follows:
s.d (X) = sqrt ( { [ (b-a) + 1 ]^2 -1 } / 12 )
s.d (X) = sqrt ( { [ (5-5) + 1 ]^2 -1 } / 12 )
s.d (X) = 13.28 in/s\
c) The first quartile is given by the 25% of the swipe rates lie under:
1st quartile = a + 0.25*(b-a)
1st quartile = 5 + 0.25*(50 - 5)
1st quartile = 5 + 11.25 = 16.25 in/s
d) The third quartile is given by the 75% of the swipe rates lie under:
3rd quartile = a + 0.75*(b-a)
3rd quartile = 5 + 0.75*(50 - 5)
3rd quartile = 5 + 33.75 = 38.75 in/s
e) what percentage of subway riders must re-swipe the card because they were outside the acceptable range?
1 - P(10<= x <=40) =
1 - (30/45) = 1 - 2/3 = 1/3 = 33.33%
