6.41 Probability or Measurement (Inverse)? (Example8 0) The Normal model /(69, 3) describes the distribution of male heights in the United States. Which of the following questions asks for a probability, and which asks for a measurement? Identify the type of problem and then answer the given question. Density 69 Answer 78 Question Suppose the Tall Club of Silicon Valley wanted to admit the tallest 2% of men. What minimum height requirement should the club set for its membership criteria? Answer this question by following the numbered steps. Step 1 Think about it. Will the height be above the mean or below it? Explain. Step 2 Label z-scores. Label the curve with integer z-scores. The tick marks represent the position of integer z-scores from -3 to 3. Step 3 Draw a vertical line in the graph and shade the sketch. The tallest 2% of men are in the right tail of the distribution. Draw a vertical line at the approximate location of the height that separates the tallest 2% of men (to the right of the line) from the shortest 98% of men (to the left of the line) and shade the area to the right of the line. The line should be somewhere between a z-score of 2 and 3. Step 4 C Find the height. The height can be found using technology (an inverse Normal problem) or using a Normal table. To use a Normal table, locate the area closest to 0.9800. Report the z-score for that area. Then find the height that corresponds to the z-score using the formula I = / + 20 Step 5 Add the height to the sketch. Add the height on the sketch where it says "Answer." Step 6 Write a sentence. Finally, write a sentence stating what you found