A vertical line is drawn through a normal distribution so that the proportion in the tail is 0.1841.The line was drawn at z = 0.90 or at z = -0.90.

Question

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Since the total area under a normal distribution curve is 1, the proportion in the tail on one side of the vertical line at z = 0.90 or z = -0.90 is (1-0.1841)/2 = 0.40795. Using a standard normal distribution table or calculator, we can find that the z-score for this proportion is approximately 0.25. This means that the vertical line is located at a distance of 0.25 standard deviations away from the mean. Since the normal distribution is symmetric, the same holds true for the other side of the distribution. Therefore, the line was drawn at z = 0.90 - 0.25 = 0.65 or z = -0.90 + 0.25 = -0.65.

Since both of these values are within the range of the standard normal distribution (i.e. between -3 and 3), it is possible to draw a line through the normal distribution at either of these points to obtain the desired proportion in the tail. Therefore, the statement is true and the answer is A.

A Vertical Line Is Drawn Through a Normal Distribution So