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Chapter 2: Q 3.3. (page 98)

Now suppose that you convert the class鈥檚 heights to z-scores. What would be the shape, center, and spread of this distribution? Explain.

Short Answer

Expert verified

Mean will become 0 (zero) and standard deviation would be 1 (one)

Step by step solution

01

Step 1. Given

02

Step 2. Concept

The following Minitab computer output validates the outcome: When each observation in distribution is standardized, the resultant set of z-scores has a mean of 0 and a standard deviation of 1

03

Step 3. Explanation

Height is now measured in z-scores. The shape will not be modified by the transformation from height to z-scores, therefore the shape will not be changed, but the mean will be shifted to 0 (zero) and the standard deviation will become1based on the given data (one)

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Most popular questions from this chapter

T2.4. The figure shows a cumulative relative frequency graph of the number of ounces of alcohol consumed per week in a sample of 150adults. About what percent of these adults consume between 4and 8ounces per week?

(a)20%(b)40%(c)50%(d)60%(e)80%

Use Table A to 铿乶d the value zfrom the standard Normal distribution that satis铿乪s each of the following conditions. In each case, sketch a standard Normal curve with your value of zmarked on the axis. Use your calculator or the Normal Curve applet to check your answers.

Working backward

(a) The 10th percentile.

(b) 34% of all observations are greater thanz.

The distribution of heights of young women aged 18to 24is approximately N(64.5,2.5)

1. Sketch a Normal density curve for the distribution of young women's heights. Label the points one, two, and three standard deviations from the mean.

About what proportion of observations lie between 7and 8?

Measuring bone density Individuals with low bone density have a high risk of broken bones (fractures). Physicians who are concerned about low bone density (osteoporosis) in patients can refer them for specialized testing. Currently, the most common method for testing bone density is dual-energy X-ray absorptiometry (DEXA). A patient who undergoes a DEXA test usually gets bone density results in grams per square centimeter(g/cm2)and in standardized units. Judy, who is 25years old, has her bone density measured using DEXA. Her results indicate a bone density in the hip948g/cm2and a standardized score ofz=鈭�1.45. In the reference population of For 25-year-old women like Judy, the mean bone density in the hip is 956g/cm2

(a) Judy has not taken a statistics class in a few years. Explain to her in simple language what the standardized score tells her about her bone density.

(b) Use the information provided to calculate the standard deviation of bone density in the reference population.
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