Question 1170928
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) = 52 pounds
* Standard deviation (σ) = 6.6 pounds

**Using a Graphing Calculator**

We'll use the `normalcdf` function:

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

**Calculations**

**a) Percentage of dogs weighing less than 52 pounds**

* We want P(X < 52).
* `lower_bound`: -1E99 (or a very small number)
* `upper_bound`: 52
* `mean`: 52
* `standard_deviation`: 6.6

    * `normalcdf(-1E99, 52, 52, 6.6)`
    * Result: approximately 0.5

* Percentage: 0.5 \* 100% = 50.0%

**b) Percentage of dogs weighing less than 49 pounds**

* We want P(X < 49).
* `lower_bound`: -1E99 (or a very small number)
* `upper_bound`: 49
* `mean`: 52
* `standard_deviation`: 6.6

    * `normalcdf(-1E99, 49, 52, 6.6)`
    * Result: approximately 0.32044

* Percentage: 0.32044 \* 100% ≈ 32.0%

**c) Percentage of dogs weighing more than 49 pounds**

* We want P(X > 49).
* `lower_bound`: 49
* `upper_bound`: 1E99 (or a very large number)
* `mean`: 52
* `standard_deviation`: 6.6

    * `normalcdf(49, 1E99, 52, 6.6)`
    * Result: approximately 0.67956

* Percentage: 0.67956 \* 100% ≈ 68.0%

**Answers**

* a) 50.0%
* b) 32.0%
* c) 68.0%