In a survey of a group of men, the heights in the 20-29 age group were normally
ID: 3319571 • Letter: I
Question
In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.768.7 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 65 inches. The probability that the study participant selected at random is less than 65 inches tall is nothing. (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 65 and 71 inches. The probability that the study participant selected at random is between 65 and 71 inches tall is nothing. (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 71 inches. The probability that the study participant selected at random is more than 71 inches tall is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning.
Explanation / Answer
A) P(X < 65)
= P((x - mean)/SD < (65 - mean)/SD)
= P(Z < (65 - 68.7)/2)
= P(Z < -1.85)
= 0.0322
B) P(65 < x < 71)
= P((65 - 68.7)/2 < Z < (71 - 68.7)/2)
= P(-1.85 < Z < 1.15)
= P(Z < 1.15) - P(Z < -1.85)
= 0.8749 - 0.0322
= 0.8427
C) P(X > 71)
= P(Z > (71 - 68.7)/2)
= P(Z > 1.15)
= 1 - P(Z < 1.15)
= 1 - 0.8749
= 0.1251
D) P(x < 65) = 0.0322 which is less than 0.05, so it is unusual.
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