The mean height of adult men is about 175 centimeters (cm) with standard deviati

Question

The mean height of adult men is about 175 centimeters (cm) with standard deviation 7 cm. The mean height of adult women is about 160 cm with standard deviation 6 cm. If a man and a woman are both 166.5 cm tall, which is person's height is more rare with respect to other people of the same sex? A health researcher is curious about the heights of first-year college students. Suppose that the mean height of all first-year students is mu = 68.5 inches with standard deviation sigma = 4.5 inches, and that the heights follow a Normal distribution. (a) How likely is it that one randomly selected student has height 62 inches or less? (b) How likely is it that a sample of 30 randomly selected first-year students has mean height of 62 inches or less?

Explanation / Answer

7) Z = (X -mean)/sd

we have to check z-scores ,

hence

z1 = (166.5 -175)/7 = -1.214285

z2 = (166.5 - 160)/ 6 = 1.083333

far is |z| , rarer it is .

since |z1 | > |z2|

man's height is more rare with respect to other people of the same sex.

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