(i. The proportion of the area under a normal curve to the right of z = -1.21 is 0.8869. (ii) The proportion of the area under a normal curve to the left of z = 0.50 is 0.1914.
(iii) The proportion of the area under a normal curve to the left of z = -2.10 is 0.0179.
A) (i), (ii), and (iii) are all correct statements
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (ii) and (iii) are correct statements but not (i).

Question

Quizplus · Accepted Answer

The proportion of the area under a normal curve to the right of z = -1.21 is indeed 0.8869 because the area to the left of z = -1.21 is 0.1131 (1 - 0.8869), reflecting the lower tail probability for a z-score of -1.21. The statement about the proportion to the left of z = 0.50 being 0.1914 is incorrect; the correct proportion is approximately 0.6915, as z = 0.50 is above the mean, indicating a majority area to the left. The proportion to the left of z = -2.10 being 0.0179 is correct, as this represents a very small area under the curve, consistent with the extreme negative z-score indicating a position far below the mean.

(I the Proportion of the Area Under a Normal Curve