Question

what is the approximate area of the unshaded region under the standard normal curve below? use the portion of the standard normal table given to help answer the question.

Explanation:

Step1: Identify Z - value from graph

The shaded region seems to end at \( z = 1 \) (assuming the x - axis labels, and typical standard normal curve interpretation). Wait, actually, looking at the table, we need to find the area corresponding to the z - value. Wait, maybe the shaded region is from the left up to \( z = 1 \)? Wait, the standard normal table: for \( z = 0.00 \), probability is 0.5000, for \( z = 1.00 \), the probability (area to the left) is 0.8413? Wait, no, maybe the graph is shaded from, say, \( z=-3 \) to \( z = 1 \)? Wait, the x - axis has labels - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4. The shaded region is a dark area. Wait, maybe the z - value at the right end of the shaded region is \( z = 1 \). Let's recall the standard normal table. The area to the left of \( z = 1 \) is 0.8413, but if the shaded region is from, say, \( z=- \infty \) to \( z = 1 \), but maybe the graph is shaded from, for example, the left tail up to \( z = 1 \). Wait, the table given has \( z = 0.00 \) with probability 0.5000, and maybe another row (partially visible) for \( z = 1.00 \) with probability 0.8413? Wait, the problem is about the area of the unshaded region? Wait, no, the question is "What is the approximate area of the unshaded region under the standard normal curve below?" Wait, maybe I misread. Wait, the standard normal curve is symmetric around \( z = 0 \). If the shaded region is, say, from \( z=-3 \) to \( z = 1 \), but the table is given. Wait, maybe the z - value at the boundary of the shaded and unshaded region is \( z = 1 \). The area to the left of \( z = 1 \) is 0.8413, so the unshaded area below (wait, "below" the curve? No, the area under the curve. Wait, maybe the unshaded region is to the right of \( z = 1 \). The total area under the curve is 1. So the area to the right of \( z = 1 \) is \( 1 - 0.8413=0.1587 \), but maybe the z - value is different. Wait, the table has \( z = 0.00 \) with probability 0.5000. Wait, maybe the shaded region is from \( z=- \infty \) to \( z = 1 \), so the unshaded region is to the right of \( z = 1 \). But the question says "the unshaded region under the standard normal curve below" – maybe "below" is a typo, or "to the right". Wait, let's assume that the boundary of the shaded and unshaded region is at \( z = 1 \). The area to the right of \( z = 1 \) is \( 1 - P(Z\leq1) \). From the standard normal table, \( P(Z\leq1)=0.8413 \), so the unshaded area is \( 1 - 0.8413 = 0.1587 \), approximately 0.1587 or 0.16. But maybe the z - value is 1.00. Wait, the table given has \( z = 0.00 \) with probability 0.5000, and the next row (partially visible) has \( z = 1.00 \) with probability 0.8413? Wait, the second row (partially) shows "1.00" and "0.8413"? So if the shaded region is to the left of \( z = 1 \), then the unshaded region below (wait, "below" – maybe the unshaded region is to the right of \( z = 1 \), so the area is \( 1 - 0.8413 = 0.1587\approx0.16 \). But maybe the z - value is 1.00. So the unshaded area (to the right of \( z = 1 \)) is approximately 0.16 (or 0.1587).

Wait, maybe the graph is shaded from, say, \( z=- \infty \) to \( z = 1 \), so the unshaded area is to the right of \( z = 1 \), which is \( 1 - 0.8413 = 0.1587\approx0.16 \).

Step2: Calculate unshaded area

The total area under the standard normal curve is 1. If the area to the left of \( z = 1 \) (shaded) is 0.8413, then the unshaded area (to the right of \( z = 1 \)) is \( 1 - 0.8413=0.1587\approx0.16 \) (or more precisely, 0.1587).

Answer:

The approximate area of the unshaded region is \( \boldsymbol{0.1587} \) (or approximately \( \boldsymbol{0.16} \))