Question

Suppose that the average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution with mean 6.1 and standard deviation 1.0. The middle 50% of patients sleep between 5.42 hours and what other length of time? Answers should be correct to two decimal places.

Answer 1

To find the other length of time for which 50% of the patients sleep, find the corresponding z-scores for the lower and upper percentages of the normal distribution curve. The middle 50% of the patients sleep between 5.42 hours and the other length of time.

Step-by-step explanation:

To find the other length of time for which 50% of the patients sleep, we need to find the corresponding z-scores for the lower and upper percentages of the normal distribution curve. The middle 50% of the patients corresponds to the area between the z-scores of -0.674 and 0.674.

Using the z-score formula:

z = (x - mean) / standard deviation,

we can solve for x:

-0.674 = (x - 6.1) / 1.0

x = -0.674 * 1.0 + 6.1 = 5.426

Therefore, the middle 50% of patients sleep between 5.42 hours and 6.78 hours (rounded to two decimal places).