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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

In Exercises 9鈥�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).

In Exercises 9鈥�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.

Distributions In a continuous uniform distribution,

渭=minimum+maximum2鈥�鈥�鈥�and蟽=range12

a. Find the mean and standard deviation for the distribution of the waiting times represented in Figure 6-2, which accompanies Exercises 5鈥�8.

b. For a continuous uniform distribution with 渭=0鈥�鈥�鈥�and鈥�鈥�鈥�蟽=1, the minimum is-3 and the maximum is 3. For this continuous uniform distribution, find the probability of randomly selecting a value between 鈥�1 and 1, and compare it to the value that would be obtained by incorrectly treating the distribution as a standard normal distribution. Does the distribution affect the results very much?

Curving Test Scores A professor gives a test and the scores are normally distributed with a mean of 60 and a standard deviation of 12. She plans to curve the scores.

a. If she curves by adding 15 to each grade, what is the new mean and standard deviation?

b. Is it fair to curve by adding 15 to each grade? Why or why not?

c. If the grades are curved so that grades of B are given to scores above the bottom 70% and below the top 10%, find the numerical limits for a grade of B.

d. Which method of curving the grades is fairer: adding 15 to each original score or using a scheme like the one given in part (c)? Explain.

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 -1.23
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