Question

2. The amount of time a customer spends waiting for their lunch order at Harry’s Bistro is Uniformly distributed from 8 min to 20 min. A customer is chosen at random.

   1. a) Define the random variable of interest, X.

   2. b) State the distribution of X.

   3. c) Sketch the density curve, with appropriate labels.

   4. d) What is the probability that their wait time is longer than 15 minutes?

   5. e) What is the probability that their wait time is at most 11 minutes?

   6. f) What is the probability that their wait time is 14 minutes?

Answer 1

a)

X is time a customer spends waiting for their lunch order at Harry’s Bistro

b)

here X follows uniform distribution with parameter a=8 and b=20

therefore density f(X)=1/(20-8)=1/12

and cumulative distribution of F(X) =P(X<=x) =(x-a)/12 =(x-8)/12

c)

d) probability that their wait time is longer than 15 minutes =P(X>15)=1-P(X<15)=1-(15-8)/12=5/12

e) probability that their wait time is at most 11 minutes =P(X<11)=(11-8)/12=3/12=1/4

f) probability that their wait time is 14 minutes =0 (as disrete probability on a continuous distribution is 0)