1) Use z scores to compare the given values. The tallest living man at one time
ID: 3302488 • Letter: 1
Question
1) Use z scores to compare the given values. The tallest living man at one time had a height of 270 cm. The shortest living man at that time had a height of 105.8 cm. Heights of men at that time had a mean of 174.66 cm and a standard deviation of 8.76 cm. Which of these two men had the height that was more extreme?
Since the z score for the tallest man is z = ___? and the z score for the shortest man is z = ___? The [TALLEST or SHORTEST] was more extreme.
2) In a recent awards ceremony, the age of the winner for best actor was 26 and the age of the winner for best actress was 50. For all best actors, the mean age is 41.8 years and the standard deviation is 8.2 years. For all best actresses, the mean age is 37.1 years and the standard deviation is 11.6 years. Relative to their genders, who had the more extreme age when winning the award, the actor or the actress?
Since the z score for the actor man is z = ___? and the z score for the actress man is z = ___? The [ACTOR or ACTRESS] was more extreme.
Explanation / Answer
Z score = (score - mean)/ standard deviation
1) z score for the tallest man = (270-174.66)/8.76 = 10.88
Z score for the shortest man = (105.8 - 174.66)/8.76 = -7.86
The TALLEST was more extreme
2) The z score for the actor man = (26 - 41.8)/8.2 = -1.93
Z score for the actress = (50 - 37.1)/11.6 = 1.11
The ACTOR was more extreme
(The sign of z score doesnt matter when we want to see if a score is extreme)
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