Final answer:
To determine the probability that a patient's recovery time is between 4 and 7 days, we must calculate the Z-scores for these values and then find the probability using a Z-table or technology, based on the normal distribution with a mean of 5.8 days and a standard deviation of 1.6 days.
Step-by-step explanation:
The question pertains to the application of normal distribution to calculate the probability that a patient's recovery time after a surgical procedure is within a specific range. Given the mean (μ) is 5.8 days and the standard deviation (σ) is 1.6 days, using the Z-score formula for normal distribution, we can find the Z-scores for 4 and 7 days and then use a Z-table or technology to find the probability that a recovery time falls between these two values.
To calculate the Z-scores:
- Z for 4 days = (4 - 5.8) / 1.6
- Z for 7 days = (7 - 5.8) / 1.6
After finding the Z-scores, we check a Z-table or use technology, like a graphing calculator or statistics software, to find the area between these two Z-scores, which represents the probability of a recovery time between 4 and 7 days.