The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 1.8 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X- N( 4 1.8 b. What is the median recovery time? 4 days c. What is the Z-score for a patient that took 5.7 days to recover? 0.9444 d. What is the probability of spending more than 3 days in recovery? e. What is the probability of spending between 3 and 3.5 days in recovery? f. The 85th percentile for recovery times is days.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Given:
Let X represent the patients time from a particular surgical procedure.
μ = 4
σ = 1.8
Thus, X~N(μ = 4, σ = 1.8)
Part d:
The probability of spending more than 3 days in recovery is computed as,
Thus, the probability of spending more than 3 days in recovery is 0.7108.
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