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Chapter 6: Q6.4 (page 260)

The percentage of all possible observations of the variable that lie between 7 & 12 equals the area under its density curve between _ and _, expressed as a percentage.

Short Answer

Expert verified

Percentage of total observations that lie between 7 & 12 equals the area under density curve between x > 7 & x <10 expressed as a percentage

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 = 45.3 Kgs

02

Density Curve Probability 

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

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

03

Explanation

The percentage of all possible observations of the variable that lie between 7 & 12 equals the area under its density curve between x> 7 & x < 12

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Most popular questions from this chapter

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?

In Exercises 11–14, use the population of {34, 36, 41, 51} of the amounts of caffeine (mg/12oz) in Coca-Cola Zero, Diet Pepsi, Dr Pepper, and Mellow Yello Zero.

Assume that  random samples of size n = 2 are selected with replacement.

Sampling Distribution of the Median Repeat Exercise 11 using medians instead of means.

In Exercises 13–20, use the data in the table below for sitting adult males and females (based on anthropometric survey data from Gordon, Churchill, et al.). These data are used often in the design of different seats, including aircraft seats, train seats, theater seats, and classroom seats. (Hint: Draw a graph in each case.)

Mean

St.Dev.

Distribution

Males

23.5 in

1.1 in

Normal

Females

22.7 in

1.0 in

Normal

For males, find P90, which is the length separating the bottom 90% from the top 10%.

Significance For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are

a. significantly high (or at least 2 standard deviations above the mean).

b. significantly low (or at least 2 standard deviations below the mean).

c. not significant (or less than 2 standard deviations away from the mean).
See all solutions

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