Question

A subway train on the Red Line arrives every 12 minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a unifrom distribution.

A) give the distribution of X

B) graph the probability distribution

C) F(x) = ____ , where ___ < x ___

D) μ =

E) σ =

F) find the probability that a commuter waits less than 1 minutes

G) find the probability that a commuter waits between four and five minutes

H) State "70% of all commuters wait more than how long for the train?" in a probability question. Find the probability that the commuter waits more than ___ minutes. Draw the pictire and find the probability.

Answer 1

a)

here for uniform distribution parameter a =0 and b=12

pdf of X:

f(x)=1/(b-a) =

1/12    for 0 <x<12

b)

c)

F(x) =x/12 where 0<X <12

d)

mean μ=(a+b)/2 =

6

e)

standard deviation σ=(b-a)/√12=

3.4641

f)

P(X<1)=(1-0)/12=0.0833

g)

P(4<X<5)=(5-4)/12=0.0833

h)

Find the probability that the commuter waits more than 3.6 minutes