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Chapter 6: Q6.12 (page 260)

A curve has area 0.425to the left of 4and area 0.585to the right of 4. Could this curve be a density curve for some variable ? Explain your answer

Short Answer

Expert verified

No, the curve having area 0.425and 0.585area to right & left of point 4cannot be a density curve.

Step by step solution

01

Density Curve Concept 

Density Curve is a graphical representation of numerical distribution, having variable outcomes that are continuous (which can take non whole values), like weight = 54.3Kgs

02

Density Curve Probability 

It shows likelihood ( probability) of continuous variable' outcomes. As total probability = 1total area under the curve is also equal to1

Percentage of total observations that lie within a range is equal to percentage of area under the curve between the corresponding values.

03

Explanation  

As the area under the curve to the right and left of 4=0.585and ; so total area is = 0.585+0.425=1.01

Since total area under the curve = 1.01, which is not equal to 1. Hence, it can't be a density curve for a variable.

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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 0

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.

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.

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.

Finding Bone Density Scores. In Exercises 37–40 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 P99, the 99th percentile. This is the bone density score separating the bottom 99% from the top 1%.
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