According to numerous online resources, the mean height for American women is 5

Question

According to numerous online resources, the mean height for American women is 5 feet 5 inches, with a standard deviation of 3.5 inches. Use the empirical rule to find the probability that a randomly chosen American woman is between 5 feet 1.5 inches and 5 feet 8.5 inche 3. Write an expression of the form Pinequality) that represents the probability you found in Question 2. Use h to -3.5 inch YS represent the height of a randomly chosen woman, and write heights in inches. diagram that illustrates the empirical rule.) ould you expect to be taller than 6 eet? (You'll need to interpret the

Explanation / Answer

Question 2

Mean height of AMerican women = 5 feet 5 inches

standard deviation = 3.5 inches

Here as per empirical rule, The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule said that 68% of data falls within the first standard deviation from the mean.

so Here the one standard deviation away is +-

so (5 feet 1.5 inch to 5 feet 8.5 inch)

so there are 68% of values are in between these two.

Question 2

Here the probaability expression in mathematically

Pr(61.5 inch < h < 68.5 inch; 65 inch) = Norm(61.5 inch < h < 68.5 inch; 65 inch ; 3.5 inch) = 0.68

Question 3

Here Pr(h > 72 inch) = 1 - Pr(h < 72 inch)

Z = (72 - 65)/ 3.5 = 2

Pr(Z <2) = 0.9773

Pr(h > 72 inch) = 1 - Pr(h < 72 inch) = 1 - 0.9773 = 0.0227

so out of 500 women , we expect number of women to be taller tha 6 feet = 500 * 0.0227 = 11.35 women or 12 women.

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