Problem

The healing time of a certain type of incision is normally distributed with an average healing time of 192 hours and a standard deviation of 20 hours. What percentage of the people having this incision would heal in 6 days or less? The percentage of the people having this incision that would heal in 6 days or less is $\%$. (Type an integer or decimal rounded to two decimal places as needed.)

Solution

Step 1 :First, we need to convert the 6 days into hours since the average healing time and standard deviation are given in hours. There are 24 hours in a day, so 6 days is 144 hours.

Step 2 :Next, we need to calculate the z-score. The z-score is a measure of how many standard deviations an element is from the mean. The formula for the z-score is \((X - μ) / σ\), where X is the value we are looking for, μ is the mean, and σ is the standard deviation.

Step 3 :Substitute the given values into the z-score formula: \((-2.4) = (144 - 192) / 20\).

Step 4 :After we find the z-score, we can look up this value in a standard normal distribution table to find the percentage of people who would heal in 6 days or less. The percentage is approximately 0.82%.

Step 5 :However, the question asks for the answer to be rounded to two decimal places. Therefore, we need to round our answer. The rounded percentage is 0.82%.

Step 6 :Final Answer: The percentage of the people having this incision that would heal in 6 days or less is approximately \(\boxed{0.82\%}\).

From Solvely APP
Source: https://solvelyapp.com/problems/33749/

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