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Chapter 6: Q6.7 (page 260)

The area under the density curve that lies to the right of 15 is 0.324. What percentage of all possible observations of the variable

a. exceed 15 ?

b. are at most 15 ?

Short Answer

Expert verified

Percentage of variable's observations that exceed 15=32.4%

Percentage of variable's observations that are at most15=67.6%

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 =45.3Kgs

02

Density Curve Probability

It shows likelihood ( probability) of continuous variable' outcomes. As total probability = 1, total 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 under the density curve that lies to the right of 15=0.324out of total area = 1, so percentage of observations more than 15=32.4%

Hence, percentage of observations that are at most 15include observations that are less than or equal to 15. These observations are to the left of 15, so 1-0.324=67.6%

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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).

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).

Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45鈥�48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2.

About______ % of the area is between z = -2 and z = 2 (or within 2 standard deviation of the mean).

In Exercises 7鈥�10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.

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a. Find the value of the population variance 蟽2.

b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample variance s2. Then combine values of s2that are the same, as in Table 6-3 (Hint: See Example 2 on page 258 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.)

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d. Based on the preceding results, is the sample variance an unbiased estimator of the population variance? Why or why not?

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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?
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