Question 1170930
Here's how to solve this problem using the properties of a normal distribution:

**Understanding the Problem**

* We have a normal distribution.
* Mean (μ) = 6 days
* Standard deviation (σ) = 1.7 days

**Using a Graphing Calculator**

Most graphing calculators (like TI-84, etc.) have built-in functions to calculate probabilities for normal distributions. Here's the general process:

1.  **Access the Normal Distribution Function:**
    * Look for a "DISTR" or "Distribution" menu.
    * Find "normalcdf" (normal cumulative distribution function).

2.  **Input the Values:**
    * `normalcdf(lower_bound, upper_bound, mean, standard_deviation)`

**Calculations**

**a) Probability of spending less than 6 days in recovery**

* We want P(X < 6), where X is the recovery time.
* `lower_bound`: A very small number (e.g., -1E99 or -10000) to represent negative infinity.
* `upper_bound`: 6
* `mean`: 6
* `standard_deviation`: 1.7

    * `normalcdf(-1E99, 6, 6, 1.7)`
    * The result will be approximately 0.5

* Percentage: 0.5 \* 100% = 50.0%

**b) Probability of spending more than 4 days in recovery**

* We want P(X > 4)
* `lower_bound`: 4
* `upper_bound`: A very large number (e.g., 1E99 or 10000)
* `mean`: 6
* `standard_deviation`: 1.7

    * `normalcdf(4, 1E99, 6, 1.7)`
    * The result will be approximately 0.88079

* Percentage: 0.88079 \* 100% ≈ 88.1%

**c) Probability of spending between 4 days and 6 days in recovery**

* We want P(4 < X < 6)
* `lower_bound`: 4
* `upper_bound`: 6
* `mean`: 6
* `standard_deviation`: 1.7

    * `normalcdf(4, 6, 6, 1.7)`
    * The result will be approximately 0.38079

* Percentage: 0.38079 \* 100% ≈ 38.1%

**Answers**

* a) 50.0%
* b) 88.1%
* c) 38.1%