41. Where's the bus? Sally takes the same bus to work
pgill every morning. The amount of time (in minutes)
that she has to wait for the bus can be modeled by a
uniform distribution on the interval from 0 minutes to
10 minutes.
(a) Draw a density curve to model the amount of time that
Sally has to wait for the bus. Be sure to include scales
on both axes.
(1) On about what percent of days does Sally wait between
2.5 and 5.3 minutes for tlic bus?
(c) Find the 70th percentile of Sally's wait times.

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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