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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

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).

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.

If bone density scores in the bottom 2% and the top 2% are used as cutoff points for levels that are too low or too high, find the two readings that are cutoff values.

Continuous Uniform Distribution. In Exercises 5鈥�8, refer to the continuous uniform distribution depicted in Figure 6-2 and described in Example 1. Assume that a passenger is randomly selected, and find the probability that the waiting time is within the given range.


Less than 4.00 minutes

Sampling with Replacement The Orangetown Medical Research Center randomly selects 100 births in the United States each day, and the proportion of boys is recorded for each sample.

a. Do you think the births are randomly selected with replacement or without replacement?

b. Give two reasons why statistical methods tend to be based on the assumption that sampling is conducted with replacement, instead of without replacement.

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.

Greater than 0
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