Question

2. The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.

a. What is the z-score for a patient who takes ten days to recover?
b. What percentage of patients recover in less than 10 days?

Answer 1

The z-score for a patient who takes ten days to recover is 2.33. Approximately 99.08% of patients recover in less than 10 days.

Step-by-step explanation:

a. To calculate the z-score, we use the formula: z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (10 - 5.3) / 2.1 = 2.33.

b. To find the percentage of patients who recover in less than 10 days, we need to find the area under the normal distribution curve to the left of 10. Using a standard normal table or a statistical calculator, we find that the area is approximately 0.9908 or 99.08%.