3.12 APPLY YOUR KNOWLEDGE Use the Normal Table. Use Table A to find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is the answer to the question.

(a) z

(b) z > −1.58

(c) z

(d) −0.42

(a) In the drought year 1987, 697 mm of rain fell. In what percent of all years will India have 697 mm or less of monsoon rain?

(b) “Normal rainfall” means within 20% of the long-term average, or between 682 mm and 1022 mm. In what percent of all years is the rainfall normal? The Medical College Admissions Test. Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). 8 A new version of the exam was introduced in spring 2015 and is intended to shift the focus from what applicants know to how well they can use what they know. One result of the change is that the scale on which the exam is graded has been modified, with the total score of the four sections on the test ranging from 472 to 528. In spring 2015, the mean score was 500.0 with a standard deviation of 10.6.

(a) What proportion of students taking the MCAT had a score over 510?

(b) What proportion had scores between 505 and 515?

3.13 Table A. Use Table A to find the value z of a standard Normal variable that satisfies each of the following conditions. (Use the value of z from Table A that comes closest to satisfying the condition.) In each case, sketch a standard Normal curve with your value of z marked on the axis. (a) The point z with 75% of the observations falling below it (b) The point z with 15% of the observations falling above it (c) The point z with 15% of the observations falling below it 3.14 The Medical College Admissions Test. A new version of the Medical College Admissions Test (MCAT) was introduced in spring 2015 and is intended to shift the focus from what applicants know to how well they can use what they know. One result of the change is that the scale on which the exam is graded has been modified, with the total score of the four sections on the test ranging from 472 to 528. In spring 2015, the mean score was 500.0 with a standard deviation of 10.6.