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Chapter 6: Q6.3 (page 259)

Short Answer

Expert verified

Variable having density curve - has percentage of observations lie within a range equal to corresponding area between those values in its density curve.

Step by step solution

01

Density Curve Concept 

A Density Curve is a graphical representation of numerical distribution, having variable outcomes that are continuous (which can take non whole values). Eg - weight = 54.3 kgs

  • It shows likelihood ( probability) of continuous variable' outcomes. As total probability = 1, total area under the curve is also equal to 1.
02

Explanation 

For a density curve, percentage of all possible observations of the variable that lie within a specified range is Equal to percentage of total area under the corresponding range.

  • Eg : Probability (X > or < 5) = Probability (Percentage of total area under the curve, where x > 5 or x < 5 respectively)

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Most popular questions from this chapter

Standard normal distribution, 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 4.55

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 21–24, use these parameters (based on Data Set 1 “Body Data” in Appendix B):• Men’s heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in.• Women’s heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.Mickey Mouse Disney World requires that people employed as a Mickey Mouse character must have a height between 56 in. and 62 in.

a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as Mickey Mouse characters?

b. If the height requirements are changed to exclude the tallest 50% of men and the shortest 5% of men, what are the new height requirements?

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.

Birth Weights Based on Data Set 4 “Births” in Appendix B, birth weights are normally distributed with a mean of 3152.0 g and a standard deviation of 693.4 g.

a. For the bell-shaped graph, what is the area under the curve?

b. What is the value of the median?

c. What is the value of the mode?

d. What is the value of the variance?
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