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 69.8 inches and a standard deviation of 4.0 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 is (Round 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 s 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. The event in part (a) is unusual because its probability is less than 0.05 B. There are no unusual events because all the probabilities are greater than 0.05 C. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05 D. The events in parts (a) and (c) are unusual because its probabilities are less than 0.05.

Explanation / Answer

mean = 69.8 ,sd= 4

Z = (X- 69.8)/4

a)

P(X<67) = P(Z< -0.7) = 0.242

b) P(67 <X< 72)

=P ( 0.7<Z<0.55 )=0.4668

c)

P(X> 72) = P (Z>0.55)=0.2912

d) none of the events are unusual as p > 0.05

hence option B) is correct

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