Final answer:
To find the z-score corresponding to an area of 0.9616 to the left of the value, you would refer to a z-table and identify the z-score that is approximately 1.75. You can then create a graph with the x-axis for z-scores and y-axis for probability density, where the total area under the curve represents a probability of 1.
Step-by-step explanation:
Finding the z-score in a Standard Normal Distribution
To find the z-score corresponding to an area of 0.9616 in a standard normal distribution, where the mean is 0 and the standard deviation is 1, we use a z-table or z-score table. Locating the closest area to 0.9616 in the z-table gives us a z-score of approximately 1.75. This is because the standard normal distribution table lists the cumulative area from the far left of the distribution up to a given z-score, and finding the area closest to 0.9616 will provide the z-score associated with that cumulative probability.
To create the graph of the standard normal distribution, plot a symmetric bell-shaped curve centered at the mean (0), with the x-axis representing the z-scores and the y-axis representing the probability density. The area under the curve to the left of the z-score of 1.75 would represent the given area of 0.9616, while the area under the entire curve represents the total probability of 1.