the average healing time of a certain type of incision is 192 hours, with standard deviation of 15 hours…

the average healing time of a certain type of incision is 192 hours, with standard deviation of 15 hours. what percentage of the people having this incision would heal in 6 days or less? assume a normal distribution. click the icon to view the area under the standard normal curve table. % of people having this incision should heal in 6 days or less. (type an integer or decimal rounded to the nearest hundredth as needed.)
Answer
Explanation:
Step1: Convert 6 days to hours
Since 1 day has 24 hours, 6 days is $6\times24 = 144$ hours.
Step2: Calculate the z - score
The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 144$ (the value we are interested in), $\mu=192$ (the mean), and $\sigma = 15$ (the standard deviation). So $z=\frac{144 - 192}{15}=\frac{-48}{15}=-3.2$.
Step3: Find the area under the standard - normal curve
We look up the z - score of - 3.2 in the standard normal curve table. The area corresponding to $z=-3.2$ represents the percentage of people who heal in 6 days or less. From the standard normal table, the area to the left of $z = - 3.2$ is 0.0013.
Answer:
0.13%