Question

The length of time patients must wait to see a doctor in a local clinic is uniformly distributed between 15 and 45 minutes.

a. Define the random variable in words.

b. What is the probability of a patient waiting exactly 30 minutes?

c. What is the probability that a patient would have to wait between 5 and 25 minutes?

d. Compute the probability that a patient would have to wait over 30 minutes. e. Determine the expected waiting time and its standard deviation.

Answer 1

Let ,

The PDF of X is ,

;

= 0 ; otherwise

a. Let , X be the continuous random variable represents the length of time patients must wait to see a doctor in a local clinic .

b. Since , the uniform distribution is continuous type distribution.

Therefore , the exact probability for continuous type distribution is zero

Therefore , P(X=30)=0

i.e. The probability of a patient waiting exactly 30 minutes is 0.

c.

Therefore , the  probability that a patient would have to wait between 5 and 25 minutes is 0.6667

d.

Therefore , the probability that a patient would have to wait over 30 minutes is 0.5.

e. Now ,

Therefore m the expected waiting time is 30 and its standard deviation is 8.66