In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts a and b below. a.) Find the probability that the participant is less than 64.5 inches?b.) Find the probability that the participant is more than 68.25 inches?

a) 20.33% probability that the participant is less than 64.5 inches.

b) 33.72% probability that the participant is more than 68.25 inches

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

a.) Find the probability that the participant is less than 64.5 inches?

This is the pvalue of Z when X = 64.5.

has a pvalue of 0.2033

20.33% probability that the participant is less than 64.5 inches.

b.) Find the probability that the participant is more than 68.25 inches?

This is 1 subtracted by the pvalue of Z when X = 68.25.

has a pvalue of 0.6628

1 - 0.6628 = 0.3372

33.72% probability that the participant is more than 68.25 inches

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