Final answer:
To determine the probabilities related to the patient recovery time, calculate the Z-scores for the given values and reference a normal distribution table or computational tool. For each scenario, the corresponding cumulative probability returns the required likelihood in percentage form.
Step-by-step explanation:
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.7 days and a standard deviation of 1.7 days. To find the probabilities associated with this normal distribution, we can use the Z-score formula, Z = (X - μ) / σ, where X is the value of interest, μ is the mean, and σ is the standard deviation.
- (a) To find the probability of spending less than 9 days in recovery, calculate the Z-score for X = 9 and then use a normal distribution table or software to find the cumulative probability.
- (b) To find the probability of spending more than 5 days in recovery, calculate the Z-score for X = 5 and then subtract the cumulative probability from 1.
- (c) The probability of spending between 5 days and 9 days in recovery is found by calculating the cumulative probabilities for both X = 5 and X = 9 and subtracting the smaller from the larger.