# NYU Hospital waiting times

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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?

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The solution addresses the patient waiting ties at NYU hospital.

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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 ...

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- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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- "Thank you very much for your valuable time and assistance!"

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