Question

The amount of time, in minutes, that a person must wait for a taxi is uniformly distributed between 1 and 30 minutes, inclusive.

1.Find P(x<10 | x<22).

2.Find the 60th percentile.

Answer 1

Let X be the amount of time, in minutes, that a person must wait for a taxi. X is uniformly distributed between a=1 and b=30 minutes, inclusive.

the probability density fucntion (pdf) of X is

The cumulative distribution fucntion (cdf) of X is

1.Find P(x<10 | x<22).

ans: P(x<10 | x<22) = 3/7 (or 0.4286)

2.Find the 60th percentile.

Let q be the 60th percentile. That is, 60% of the observations are below q. This means that the probability of X<q is 0.60

ans: The 60th percentile is 18.4