The mean diastolic blood pressure reading for the entire student body at a large

Question

The mean diastolic blood pressure reading for the entire student body at a large western university was 85.00 mm Hg (millimeters of mercury) with an SD of 7.65. What percent of the student body measured between 70 and 80? between 90 and 100? Road tests of a certain compact car show a mean fuel rating of 30 miles per gallon, with a standard deviation of 2 miles per gallon. What percentage of these autos will achieve results of more than 35 miles per gallon? less than 27 miles per gallon? between 25 and 29 miles per gallon? between 32 and 34 miles per gallon? On a normal distribution, at what percentile must the mean fall? the median fall? the mode fall? With reference to which measure of central tendency must z scores always be computed? Approximately what percentage of the scores on a normal distribution fall below the mean? within plusminus unit from the mean? within plusminus 2 SD units from the mean?

Explanation / Answer

(10) = 85, = 7.65

(a) x1 = 70, x2 = 80

z1 = (x1 - )/ = (70 - 85)/7.65 = -1.9608 and z2 = (x2 - )/ = (80 - 85)/7.65 = -0.6536

P(70 < x < 80) = P(-1.9608 < z < -0.6536) = 0.2317 (23.17%)

(b) x1 = 90, x2 = 100

z1 = (x1 - )/ = (90 - 85)/7.65 = 0.6536 and z2 = (x2 - )/ = (100 - 85)/7.65 = 1.9608

P(90 < x < 100) = P(0.6536 < z < 1.9608) = 0.2317 (23.17%)

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