IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. (a) Find the z-score for an IQ of 99, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 99. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x- axis is the z-score. Use your z-score from part (a), rounded to one decimal place). Shade: Left of a value -1 -1.5 0 . Click and drag the arrows to adjust the values. ******** (d) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. (e) Sketch the graph, and write the probability statement. Edit Insert Formats BIUX₂ x² A - E = = E· · CORN Edit Insert Formats E (f) The middle 50% of IQs fall between what two values? - (g) Sketch the graph and write the probability statement. B I U X₂ Xº C & R 用 4 <> Σ+ Σ Α Σ+ Σ Α

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