Question

The number of minutes that a patient waits at a medical clinic to see a doctor is represented by a uniform distribution between zero and 30 minutes, inclusive.

a. If X equals the number of minutes a person waits, what is the distribution of X?

b. Write the probability density function for this distribution.

c. What is the mean and standard deviation for waiting time?

d. What is the probability that a patient waits less than ten minutes?

Answer 1

a. If X equals the number of minutes a person waits, what is the distribution of X?

X ~ U(0, 30)

b. Write the probability density function for this distribution.

f(x) = 1/(b-a) , where, a<= x <= b

= 0 , Otherwise

f(x) = 1/30 , where, 0<= x <= 30

= 0 , Otherwise

c. What is the mean and standard deviation for waiting time?

E(X) = (a+b)/2 = 30/2 = 15

V(X) = (b-a)^2/12 = 30*30/12 = 75

d. What is the probability that a patient waits less than ten minutes?

P(X<= 10) = (10-0).f(x) = 10* (1/30) = 1/3 = 033