Question 1199322
**a) Function on the Graphing Calculator**

* **Normal Cumulative Distribution Function (CDF):** You'll primarily use the normal CDF function on your calculator. This function calculates the probability that a random variable from a normal distribution falls below a certain value.

**b) Probability of Not Being Able to Stack 4 Boxes**

1. **Determine the Required Compartment Height:**
    * To stack 4 boxes, the compartment height must be greater than or equal to the sum of the heights of the four boxes. 
    * Let X1, X2, X3, and X4 represent the heights of the four boxes. 
    * Required Compartment Height ≥ X1 + X2 + X3 + X4

2. **Find the Mean and Standard Deviation of the Total Box Height:**

    * **Mean:** Since the box heights are independent and normally distributed, the mean of the sum of their heights is the sum of their individual means:
        * Mean of Total Box Height = 50 + 50 + 50 + 50 = 200 inches

    * **Variance:** The variance of the sum of independent random variables is the sum of their variances:
        * Variance of Total Box Height = 2² + 2² + 2² + 2² = 16 
        * Standard Deviation of Total Box Height = √16 = 4 inches

3. **Calculate the Probability of Insufficient Compartment Height:**

    * We need to find the probability that the sum of the box heights exceeds the compartment height.
    * Let C represent the compartment height.
    * We want to find P(C < X1 + X2 + X3 + X4) 

    * **Using the calculator's normal CDF function:**
        * Input the following:
            * Lower Bound: -∞ (or a very large negative number)
            * Upper Bound: 205 (compartment height)
            * Mean: 200 (mean of total box height)
            * Standard Deviation: 4 (standard deviation of total box height)

    * The calculator will give you the probability that the total box height exceeds the compartment height, indicating the probability that we won't be able to stack 4 boxes.

**In Summary**

* Use the normal CDF function on your calculator to find the probability that the sum of four normally distributed box heights exceeds the compartment height. 
* Remember to use the mean and standard deviation of the total box height in the calculation.

**Note:** This approach assumes that the heights of the boxes are independent of each other.