Question

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.To the left of z = -1.95

Accepted Answer

Step 1: Understand the problem. You are tasked with finding the area under the standard normal curve to the left of z = -1.95. This represents the cumulative probability for a z-score of -1.95 in a standard normal distribution. Step 2: Recall that the standard normal distribution is symmetric about the mean (z = 0), and the total area under the curve is 1. The area to the left of a given z-score represents the cumulative probability up to that z-score. Step 3: Use the z-score table (also called the standard normal table) or technology (such as a graphing calculator or statistical software) to find the cumulative probability corresponding to z = -1.95. The table or software will provide the area to the left of this z-score. Step 4: If using a z-score table, locate the row corresponding to -1.9 and the column corresponding to 0.05 (since -1.95 = -1.9 + 0.05). The intersection of this row and column gives the cumulative probability. Step 5: If using technology, input the z-score of -1.95 into the appropriate function (e.g., 'normalcdf' on a calculator or a similar function in statistical software) to directly obtain the cumulative probability. This value represents the area under the curve to the left of z = -1.95.

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

To the left of z = -1.95

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Key Concepts

Standard Normal Distribution

Z-scores

Area Under the Curve