z Scores. In Exercises 5–8, express all z scores with two decimal places.

Diastolic Blood Pressure of Females For the diastolic blood pressure measurements of females listed in Data Set 1 “Body Data” in Appendix B, the highest measurement is 98 mm Hg. The 147 diastolic blood pressure measurements of females have a mean of 70.2 mm Hg and a standard deviation of 11.2 mm Hg.

c. Convert the highest diastolic blood pressure to a z score.

검증된 단계별 안내

Step 1: Recall the formula for calculating a z-score:

z = \frac{X - μ}{σ}

, where

X

is the data value,

μ

is the mean, and

σ

is the standard deviation.

Step 2: Identify the values given in the problem:

X

(highest diastolic blood pressure) = 98 mm Hg,

μ

(mean) = 70.2 mm Hg, and

σ

(standard deviation) = 11.2 mm Hg.

Step 3: Substitute the values into the z-score formula:

z = \frac{98 - 70.2}{11.2}

Step 4: Perform the subtraction in the numerator:

98 - 70.2

Step 5: Divide the result of the subtraction by the standard deviation

11.2

to find the z-score, rounding to two decimal places.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Z Score

A z score, or standard score, indicates how many standard deviations an element is from the mean of a data set. It is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. Z scores are useful for comparing values from different distributions and understanding their relative position within a distribution.

Mean

The mean, or average, is a measure of central tendency that summarizes a set of values by dividing the sum of all values by the number of values. In the context of the diastolic blood pressure measurements, the mean provides a reference point to understand the typical blood pressure level among the sampled females. It is essential for calculating z scores, as it represents the baseline from which deviations are measured.

Standard Deviation

Standard deviation is a statistic that quantifies the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates a wider spread. In this exercise, the standard deviation of 11.2 mm Hg helps to understand how individual diastolic blood pressure measurements vary from the mean, which is crucial for calculating z scores.