SOLUTION: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5 days and standard deviation of 1.5 days. Use your graphing calculator to ans

Question 1181469: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5 days and standard deviation of 1.5 days. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent.
a) What is the probability of spending less than 9 days in recovery?
_______%
b) What is the probability of spending more than 6 days in recovery?
_______%
c) What is the probability of spending between 6 days and 9 days in recovery?
_______%
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
Here's how to solve these problems using a graphing calculator:
**a) Probability of spending less than 9 days in recovery:**
1. **Normalcdf function:** We'll use the `normalcdf` function on the calculator. This function calculates the area under a normal distribution curve between a lower and upper bound.
2. **Inputs:**
* Lower bound: Since we want the probability of *less* than 9 days, our lower bound can be a very small number (like -10000). This effectively covers the entire left tail of the distribution.
* Upper bound: 9 days
* Mean: 5 days
* Standard deviation: 1.5 days
3. **Calculator steps (may vary depending on your calculator model):**
* Press `2nd` then `VARS` to access the `DISTR` menu.
* Select `normalcdf`.
* Enter the values: `normalcdf(-10000, 9, 5, 1.5)`
* Press `ENTER`.
4. **Result:** The calculator should give you a result of approximately 0.9962. Multiply by 100 to express as a percentage: 99.62%. Rounded to the nearest tenth of a percent, this is **99.6%**.
**b) Probability of spending more than 6 days in recovery:**
1. **Normalcdf function:** We'll use `normalcdf` again.
2. **Inputs:**
* Lower bound: 6 days
* Upper bound: A very large number (like 10000) to cover the right tail of the distribution.
* Mean: 5 days
* Standard deviation: 1.5 days
3. **Calculator steps:**
* `normalcdf(6, 10000, 5, 1.5)`
4. **Result:** The calculator should give you approximately 0.2525 or **25.3%**.
**c) Probability of spending between 6 days and 9 days in recovery:**
1. **Normalcdf function:** Same as before.
2. **Inputs:**
* Lower bound: 6 days
* Upper bound: 9 days
* Mean: 5 days
* Standard deviation: 1.5 days
3. **Calculator steps:**
* `normalcdf(6, 9, 5, 1.5)`
4. **Result:** Approximately 0.7437 or **74.4%**.
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