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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

Standard Normal DistributionIn Exercises 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 scores. If using technology instead of Table A-2, round answers

to four decimal places.

Between -2.00 and 2.00.

Random Digits Computers are commonly used to randomly generate digits of telephone numbers to be called when conducting a survey. Can the methods of this section be used to find the probability that when one digit is randomly generated, it is less than 3? Why or why not? What is the probability of getting a digit less than 3?

In Exercises 5–8, 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).

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

Standard Normal Distribution. Find the indicated z score. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
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