Let \( Z \sim N(0,1) \). Which of the following is the correct shaded picture of \( P(0.51 \leq Z \leq 1.98) \) ?

1. We are given that \( Z \sim N(0,1) \), the standard normal distribution. 2. The probability of interest is \[ P(0.51 \leq Z \leq 1.98) = \Phi(1.98) - \Phi(0.51) \] where \(\Phi(z)\) denotes the cumulative distribution function of the standard normal distribution. 3. To represent \( P(0.51 \leq Z \leq 1.98) \) on the graph of the standard normal curve, you need to shade the region that lies between the vertical lines at \( z = 0.51 \) and \( z = 1.98 \). 4. This means that on the bell-shaped curve: - Draw a vertical line at \( z = 0.51 \). - Draw a vertical line at \( z = 1.98 \). - Shade the area under the curve between these two vertical lines. No shading should be outside this interval. Thus, the correct picture is the one that displays the standard normal curve with the area between \( z = 0.51 \) and \( z = 1.98 \) highlighted (shaded).