In a survey of a group of men, the heights in the 20-29 age group were normally

Question

In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.4 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 67 inches The probability that the study participant selected at random is less than 67 inches tall is (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 67 and 72 inches. The probability that the study participant selected at random is between 67 and 72 inches tall isRound to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 72 inches. The probability that the study participant selected at random is more than 72 inches tall is (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below A. O B. ° C. 0 D. The events in parts (a) and (b) are unusual because its probabilities are less than 0.05 None of the events are unusual because all the probabilities are greater than 0.05. The event in part (a) is unusual because its probability is less than 0.05 The event in part (c) is unusual because its probability is less than 0.05.

Explanation / Answer

Mean = 68.4

Sd = 2

A) P(X < 67) = P(Z < (67 - 68.4)/2)

=P(Z < - 0.7)

= 0.2420

B) P(67 < X < 72) = P((67 - 68.4)/2 < Z < (72-68.4)/2)

= P(-0.7 < Z < 1.8)

= P(Z < 1.8) - P(Z < - 0.7)

= 0.9641 - 0.2420

= 0.7221

C) P(X > 72) = P(Z > (72 - 68.4)/2)

= P(Z > 1.8)

= 1 - P(Z < 1.8)

= 1 - 0.9641

= 0.0359

D) Option-D)

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