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Chapter 6: 6.14 (page 260)

Explain in your words why a density curve has two properties listed in Key Fact 6.1 on page 252

Short Answer

Expert verified

Density curve depicts continuous outcomes probability. As probability > 0, so the curve lies on or above horizontal axis. As total probability = 1, so total area under the curve = 1

Step by step solution

01

Density Curve 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 = 54.3kgs , height = 5.4foot

02

Properties 

The curve shows likelihood ( probability) of continuous variable' outcomes.

  • A density curve is always on or above the horizontal axis - As probability of an outcome can never be negative, it is always equal to or more than 0. So, the curve is always on or above horizontal axis
  • The total area under a density curve (and above the horizontal axis) equals 1 - As total probability of all outcomes equals 1, so total area under the density curve also equal 1

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Most popular questions from this chapter

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. 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 1.28

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 -3.00 and 3.00.

In Exercises 9–12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

In Exercises 9–12, find the indicated IQ score and round to the nearest whole number. 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).
See all solutions

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