Question 1181469
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%**.