Question

The U.S. national average door-to-doctor wait time for patients to see a doctor is now 21.3 minutes. Suppose such wait times are normally distributed with a standard deviation of 6.7 minutes. Some patients will have to wait much shorter than the mean to see the doctor. Based on this information, 10% of patients will have to wait less than how many minutes to see a doctor? Round your answer in one decimal place.

Answer 1

To find the number of minutes that 10% of patients will have to wait less than, we need to use the standard normal distribution table. First, we need to find the z-score corresponding to the 10th percentile.

Using a standard normal distribution table, we find that the z-score corresponding to the 10th percentile is approximately -1.28.

We can use the z-score formula to find the corresponding raw score (number of minutes) in the distribution:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation.

Plugging in the values we have:

-1.28 = (x - 21.3) / 6.7

Solving for x:

x = -1.28 * 6.7 + 21.3

x = 12.06

Therefore, approximately 10% of patients will have to wait less than 12.1 minutes to see a doctor.