Question

41. Where's the bus? Sally takes the same bus to work

Answer 1

The density function of a continuous random variable X is called a uniform distribution when between the end points any two subintervals of the same length containing X have the same probability.

Mathematically,

f(x)= 1/b-a  , a≤ x ≤ b

     = 0 , elsewhere

She will have to 28% of the days between  2.5 and 5.3 minutes for bus.

The 70th percentile of Sally's wait is 7 minutes.

1) The percent can be found out from the area of the rectangular region where the base is in minutes.

Area = bh=1/10 (5.3-2.5)= 2.8/10= 0.28 = 28%

or

∫f(x)dx= ∫1/b-a (lim a→b)[x]= 1/10 (5.3-2.5)= 2.8/10= 0.28 = 28%

2) The 70th percentile can be found by using the same density function

∫f(x)dx= ∫1/b-a (lim a→b) [x]= 1/10 (7minutes)= 7/10= 0.7 = 70%

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