Question

1. at one major hospital in a large city, administrators keep track of the amount of time, in minutes, that patients wait in the emergency room before being seen by a doctor. it turns out the distribution of wait times at this hospital follows a symmetric bell - shaped pattern, with a mean of 42 minutes and a standard deviation of 9 minutes. isaac’s wait time is 30 minutes. which one of the following statements about isaac’s wait time is most accurate?

a. isaac’s wait time is unusual compared to other patients’ wait times.
b. isaac’s wait time is at about the 90th percentile, and this means that only about 10% of patients waited longer than isaac.
c. isaac’s wait time is at about the 10th percentile, and this means that only about 10% of patients waited for less time than isaac.
d. isaac’s wait time is at about the 10th percentile, and this means that only about 10% of patients waited longer than isaac.
e. isaac’s wait time is at about the 90th percentile, and this means that only about 10% of patients waited for less time than isaac.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value of interest, $\mu$ is the mean, and $\sigma$ is the standard deviation. Given $\mu = 42$, $\sigma=9$, and $x = 30$. Then $z=\frac{30 - 42}{9}=\frac{- 12}{9}\approx - 1.33$.

Step2: Use the standard normal distribution table

Looking up the z - score of approximately $-1.33$ in the standard - normal distribution table, the area to the left of $z=-1.33$ is about $0.0918\approx0.10$. The area to the left of a z - score in the standard normal distribution represents the percentile. So Isaac's wait time is at about the $10^{th}$ percentile, which means that only about $10\%$ of patients waited for less time than Isaac.

Answer:

C. Isaac’s wait time is at about the $10^{th}$ percentile, and this means that only about 10% of patients waited for less time than Isaac.