1. **Problem Statement:** We have three random variables \(X, Y, Z\) with normal distributions: - \(X \sim N(100, 100)\), meaning mean \(\mu_X = 100\) and variance \(\sigma_X^2 = 100\). - \(Y \sim N(300, 225)\), meaning mean \(\mu_Y = 300\) and variance \(\sigma_Y^2 = 225\). - \(Z \sim N(40, 64)\), meaning mean \(\mu_Z = 40\) and variance \(\sigma_Z^2 = 64\). We need to simulate 50 values of the random variable \(W = \frac{X + Y}{Z}\) and then prepare a histogram using class intervals of width 3. 2. **Generate the Simulation:** - Simulate 50 independent values each for \(X, Y, Z\), using their respective normal distributions. - For \(X\), use mean 100 and standard deviation \(\sigma_X = \sqrt{100} = 10\). - For \(Y\), use mean 300 and standard deviation \(\sigma_Y = \sqrt{225} = 15\). - For \(Z\), use mean 40 and standard deviation \(\sigma_Z = \sqrt{64} = 8\). 3. **Calculate the Value of W:** - For each simulated triplet \((X_i, Y_i, Z_i)\), compute \(W_i = \frac{X_i + Y_i}{Z_i}\). 4. **Prepare the Histogram:** - Determine the range of \(W\) values. - Create class intervals of width 3 covering the minimum to maximum values of \(W\). - Count how many \(W_i\) fall into each interval. - Plot the histogram accordingly. **Note:** As this is a textual explanation, the histogram plot is to be created using software like Python (matplotlib) or Excel after the simulation. **Summary:** To simulate and analyze \(W\), you: - Simulate 50 values each for \(X \sim N(100,10^2)\), \(Y \sim N(300,15^2)\), and \(Z \sim N(40,8^2)\). - Compute \(W_i = \frac{X_i + Y_i}{Z_i}\) for each set. - Create a histogram of \(W\) using class intervals of width 3. This completes the solution for the simulation and preparation of the histogram.