The director of emergency medicine at NYU hospital is studying patient waiting times. "waiting time" is defined as the time from when a patient enters the facility until he or she is seen by a physician. The study indicates that waiting time follows a normal distribution with a mean of 22 minutes and a standard deviation of 8 minutes.
a. What % of patients is seen in between 15 and 22 minutes?
b. What % of patients is seen in less than 15 minutes?
c. What % of patients is seen in more than 15 but less than 32 minutes?
d. What % of patients is seen in more than 25 but less than 32 minutes?
e. 5% of patients are seen in how many minutes or less? That is, how quickly are 5 percent of the patients seen?
Solution. Let X be a random variable representing the waiting time. It follows a normal distribution with a mean of 22 minutes and a standard deviation of 8 minutes. ie., X~N(22, 8^2)
<br>Let Y=(X-22)/8, then Y~N(0,1), ie., Y follows a standard normal distribution. We can assume the distribution function is ...
The solution addresses the patient waiting ties at NYU hospital.