Mathematics, 25.02.2020 02:55 Quizzicalkitty8

The heights of women aged 20 to 29 are symmetrically distributed with a mean of 64 inches and standard deviation of 2.7 inches. Men the same age have mean height 69.3 inches with a standard deviation of 2.8 inches. What are the z-scores for a woman 6 feet tall and a man 6 feet tall? Describe in simple language what information the z-scores give that the actual heights do not.

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Answer from: Ericapab

Z-score for 6 feet tall Women=2.96.

Z-score for 6 feet tall Men=0.96.

In a simple language z-score for men and women are telling us that height of 6 feet women is greater than other women in the population while the height of 6 feet men is not much varies to the other men in the population.

Step-by-step explanation:

Z-score for 6 feet tall Women

Z=(observed X-mean)/standard deviation

Mean=64 inches

Standard deviation=2.7 inches

X=6 feet

First we have to convert 6 feet into inches because mean and standard deviation are given in inches.

1 feet=12 inches

6 feet=12*6 inches=72 inches

X=72 inches

So,

Z=(72-64)/2.7

Z=8/2.7

Z=2.96 (rounded to two decimal places).

Z-score for 6 feet tall Men

Z=(observed X-mean)/standard deviation

Mean=69.3 inches

Standard deviation=2.8 inches

First we have to convert 6 feet into inches because mean and standard deviation are given in inches.

1 feet=12 inches

6 feet=12*6 inches=72 inches

So,

Z=(72-69.3)/2.8

Z=2.7/2.8

Z=0.96 (rounded to two decimal places).

The Z-scores tells us how the heights of the men and women who are 6 feet tall varies from the other individuals in the population.

The z-score for women 2.96 describes that a women that is 6 feet tall has much greater height than the other women as z-score lies 2.96 standard deviation above the mean.

The z-score for men 0.96 describes that a women that is 6 feet tall hasn't much greater height than the other men as z-score lies 0.96 standard deviation above the mean.

So, in a simple language z-score for men and women are telling us that height of 6 feet women is greater than other women in the population while the height of 6 feet men is not much varies to the other men in the population.

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Answer from: Quest

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