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 4 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (a) 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 (Round to four decimal places as needed) (b) Find the probability that a study participant has a height that is between 65 and 70 inches, The probability that the study participant selected at random is between 65 and 70 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 70 inches The probability that the study participant selected at random is more than 70 inches tall is (Round to four decimal places as needed) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. O A. The event in part (a) is unusual because its probability is less than 0.05 OB. The events in parts (a) and (c) are unusual because its probabilities are less than 0.05 C. There are no unusual events because all the probabilities are greater than 0.05. o

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Answer 1

The formula for z-score is -

o = Z n - X

Mean = 67.4, S.D = 3

a)

When X = 65

z = (65 - 67.4) / 3 = -2.4 / 3 = -0.8

which gives a value of 0.2119 in the z-table.

The probability of less than 65 inches is 0.2119.

b)

For X = 65, it is 0.2119.

For X = 70

z = (70 - 67.4) / 3 = 2.6 / 3 = 0.87

which gives a value of 0.8078 in the z-table.

Between 65 and 70 = 0.8078 - 0.2119 = 0.5959

The probability of between 65 and 70 inches is 0.5959.

c)

For 70, the value comes out to be 0.8078, but this is for less than 70.

More than 70 = 1 - 0.8078 = 0.1922

The probability of more than 70 inches is 0.1922.

d)

There are no unusual events as all the probabilities are more than 0.05.

Option C is the right answer.