(1 pt) The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches. Men the same age have mean height 69.3 inches with standard deviation 2.8 inches. What are thez-scores for a woman 5’8″ tall and a man 5’1″ tall? (You may round your answers to two decimal places)
z-scores for a woman 5’8″ tall: ?
z-scores for a man 5’1″ tall?
1 pt) Use Table A to find the proportion of the standard Normal distribution that satisfies each of the following statements.
Find the valuezof a standard Normal variable that satisfies each of the following conditions.
(a) The point z with 10% of the observations falling below it
(b) The point z with 50% of the observations falling above it
Use the value of from Table A that comes closest to satisfying the condition.
(a) Find the numberzsuch that the proportion of observations that are less thanzin a standard Normal distribution is 0.1004.
(b) Find the numberzsuch that 57.62% of all observations from a standard Normal distribution are greater thanz.
Automated manufacturing operations are quite precise but still vary, often with distribution that are close to Normal. The width in inches of slots cut by a milling machine follows approximately theN(0.905,0.001)distribution. The specifications allow slot widths between0.90475and0.90525. What proportion of slots meet these specifications?
Answer as a percent: ? %.
he heights of women aged 20 to 29 follow approximately the N(64, 2.58) distribution. Men the same age have heights distributed as N(69.3, 2.68). What percent of young men are shorter than the mean height of young women? %
Changing the mean and standard deviation of a Normal distribution by a moderate amount can greatly change the percent of observation in the tails. Suppose that a college is looking for applicants with SAT math scores 760 and above.
(a) In 2007, the scores of men on the math SAT followed the N(533, 116) distribution. What percent of men scored 760 or better?
(b) Women’s SAT math scores that year had the N(499, 110) distribution. What percent of women scored 760 or better?
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