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Chapter 6: Q6.2 (page 259)

State the two basic properties of every density curve.

Short Answer

Expert verified

Area under density curve represents probability, total = 1 . Mode is the highest peak of density curve, median is the value which divides curve into two equal halves.

Step by step solution

01

Basic Meaning 

A Density Curve is a graphical representation of numerical distribution, having variable outcomes that are continuous.

Continuous Outcome variables can take non whole ie decimal values.

Like weight = 54.3 kgs , height = 5.4 foot

02

Properties 

  • The curve shows likelihood ( probability) of continuous variable' outcomes. As total probability = 1, total area under the curve is also equal to 1, above the horizontal ie x axis.
  • Measures of central tendency can be located on the curve : Mode is the highest peak point of curve. Median is the point on curve, which divides it into two equal parts.

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Most popular questions from this chapter

Finding Bone Density Scores. In Exercises 37鈥�40 assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the bone density test score corresponding to the given information. Round results to two decimal places.

Find the bone density scores that can be used as cutoff values separating the lowest 3% and highest 3%.

In Exercises 5鈥�8, find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test).

Notation In general, what do the symbols 渭x炉 and 蟽x炉 represent? What are the values of 渭x炉and 蟽x炉for samples of size 64 randomly selected from the population of IQ scores with population mean of 100 and standard deviation of 15?

Using the Central Limit Theorem. In Exercises 5鈥�8, assume that females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute (based on Data Set 1 鈥淏ody Data鈥� in Appendix B).

a. If 1 adult female is randomly selected, find the probability that her pulse rate is between 78 beats per minute and 90 beats per minute.

b. If 16 adult females are randomly selected, find the probability that they have pulse rates with a mean between 78 beats per minute and 90 beats per minute.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Standard normal distribution. In Exercise 17-36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, Draw a graph, then find the probability of the given bone density test score. If using technology instead of Table A-2, round answers to four decimal places.

Less than 2.56
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