Question

Suppose that z ~ N(0, 1). Find the value such that the area of the region shaded to the right is 7%.

a) Provide a numerical answer.
b) Provide a graph, shading the appropriate region, and state the TI calculator command used to find the answer.

Answer 1

To find the z-score corresponding to an area of 7% to the right under the standard normal curve, use the TI calculator command invNorm(0.93) which yields a z-score of approximately 1.81. This score indicates the cutoff point on the standard normal curve with 93% of the area to the left and 7% to the right.

Step-by-step explanation:

You are looking to find the z-score for which the area to the right under the standard normal distribution curve is 7%. Since the total area under the curve is 1, this implies that the area to the left of the z-score is 1 - 0.07, which is 0.93. To find this z-score, you can use the TI calculator command invNorm(0.93,0,1) on a TI-83, 83+, or 84+ calculator.

This command will give you the z-score where the area to the left is 0.93. The numerical value for this z-score, according to a standard normal probability table or calculator, is approximately 1.81.

To graph this on the standard normal distribution curve, you would shade the area to the right of the z-score 1.81. The appropriate graph would show a curve representing the standard normal distribution, with the area to the right of z=1.81 shaded to indicate the 7% region.