Question 1170929
Let's solve this problem using the properties of a normal distribution and a graphing calculator.

**Understanding the Problem**

* We have a normal distribution.
* Mean (μ) = 42.7 inches
* Standard deviation (σ) = 5.7 inches

**Using a Graphing Calculator**

As before, we'll use the `normalcdf` function:

* `normalcdf(lower_bound, upper_bound, mean, standard_deviation)`

**Calculations**

**a) Percentage of years with rainfall less than 44 inches**

* We want P(X < 44).
* `lower_bound`: -1E99 (or a very small number)
* `upper_bound`: 44
* `mean`: 42.7
* `standard_deviation`: 5.7

    * `normalcdf(-1E99, 44, 42.7, 5.7)`
    * Result: approximately 0.58987

* Percentage: 0.58987 \* 100% ≈ 59.0%

**b) Percentage of years with rainfall more than 40 inches**

* We want P(X > 40).
* `lower_bound`: 40
* `upper_bound`: 1E99 (or a very large number)
* `mean`: 42.7
* `standard_deviation`: 5.7

    * `normalcdf(40, 1E99, 42.7, 5.7)`
    * Result: approximately 0.68656

* Percentage: 0.68656 \* 100% ≈ 68.7%

**c) Percentage of years with rainfall between 38 inches and 43 inches**

* We want P(38 < X < 43).
* `lower_bound`: 38
* `upper_bound`: 43
* `mean`: 42.7
* `standard_deviation`: 5.7

    * `normalcdf(38, 43, 42.7, 5.7)`
    * Result: approximately 0.33924

* Percentage: 0.33924 \* 100% ≈ 33.9%

**Answers**

* a) 59.0%
* b) 68.7%
* c) 33.9%