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 67.9 inches and a standard deviation of 3.0 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 68 inches.

(Round to four decimal places as needed.)

(b) Find the probability that a study participant has a height that is between 68 and 70 inches.

(Round to four decimal places as needed.)

(c) Find the probability that a study participant has a height that is more than 70 inches. (Round to four decimal places as needed.)

(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

A. The events in parts left parenthesis a right parenthesis and left parenthesis c right parenthesis are unusual because its probabilities are less than 0.05.

B. The events in parts left parenthesis a right parenthesis comma left parenthesis b right parenthesis comma and left parenthesis c right parenthesis are unusual because all of their probabilities are less than 0.05.

C. The event in part left parenthesis a right parenthesis is unusual because its probability is less than 0.05.

D. There are no unusual events because all the probabilities are greater than 0.05.

Explanation / Answer

Mean = 67.9
stdev = 3

a)P(X<68) = P(Z < 68-67.9/3) = P(Z<.1/3) = P(Z<.033) = .5120
b)P(68<X<70)= P(.033<Z<.7) = .525-.5120 = .0105
c)P(X>70) = P(Z>.7) = 1-.525 = .475
d) Only b part is < than .05 and therefore is the unusual event
So, C is the right answer

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