Final answer:
In order to sketch the region corresponding to the statement P(z > c)=0.45, start by considering the standard normal distribution. Shade the region to the left of c on the standard normal distribution curve.
Step-by-step explanation:
To sketch the region corresponding to the statement P(z > c) = 0.45, we need to understand the context of the problem.
- 1. The variable z represents a standard normal distribution, which has a mean of 0 and a standard deviation of 1.
- 2. The inequality z > c indicates that we are interested in the area under the curve to the right of the value c on the standard normal distribution.
- 3. The probability P(z > c) = 0.45 means that the shaded region to the right of c represents 45% of the total area under the curve.
Based on this information, we can sketch the region as follows:
1. Draw the standard normal distribution curve, which is symmetric and centered at 0.
2. Mark the value c on the x-axis, representing the boundary between the shaded region and the unshaded region.
3. Shade the area to the right of c, since we are interested in the probability of z being greater than c.
4. Adjust the position of the arrows based on the specific value of c and the desired probability (0.45 in this case).
- If the value of c is closer to the mean (0), the shaded region will be smaller and the arrows should be closer to the center.
- If the value of c is farther from the mean, the shaded region will be larger and the arrows should be farther from the center.