Chapter 6: Q. 1 (page 286)
What is a density curve, and why are such curves important?
Short Answer
The total probability under the density curve is equal to unity,

The probability distribution of body weights is depicted by the density curve above.
/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none}
Learning Materials
Features
Discover
Chapter 6: Q. 1 (page 286)
What is a density curve, and why are such curves important?
The total probability under the density curve is equal to unity,

The probability distribution of body weights is depicted by the density curve above.
All the tools & learning materials you need for study success - in one app.
Get started for free
Each year, thousands of high school students bound for college take the Scholastic Assessment Test (SAT). This test measures the verbal and mathematical abilities of prospective college students. Student scores are reported on a scale that ranges from a low of to a high of . Summary results for the scores are published by the College Entrance Examination Board in College Bound Seniors. In one high school graduating class, the SAT scores are as provided on the WeissStats site. Use the technology of your choice to answer the following questions.
a. Do the SAT verbal scores for this class appear to be approximately normally distributed? Explain your answer.
b. Do the SAT math scores for this class appear to be approximately normally distributed? Explain your answer.
A variable is normally distributed with a mean and standard deviation . Find the percentage of all possible values of the variable that
a. lie between and
b. exceed
c. are less than .
Serum Cholesterol Levels. According to the National Health and Nutrition Examination Survey, published by the National Center for Health Statistics, the serum (noncellular portion of blood) total cholesterol level of U.S. females years old or older is normally distributed with a mean of (milligrams per deciliter) and a standard deviation of . Let denote serum total cholesterol level for U.S. females 20 years old or older.
a. Sketch the distribution of the variable .
b. Obtain the standardized version, , of .
c. Identify and sketch the distribution of .
d. The percentage of U.S. females years old or older who have a serum total cholesterol level between and is equal to the area under the standard normal curve between-------- .
Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential distribution. The records also show that the mean time between arriving patients is 8 minutes.
a. Use the technology of your choice to simulate four random samples of interarrival times each.
b. Obtain a normal probability plot of each sample in part (a).
c. Are the normal probability plots in part (b) what you expected? Explain your answer.
Giant Tarantulas. One of the larger species of tarantulas is the Grammostola mollicoma, whose common name is the Brazilian giant tawny red. A tarantula has two body parts. The anterior part of the body is covered above by a shell, or carapace. From a recent article by F. Costa and F. Perez-Miles titled "Reproductive Biology of Uruguayan Theraphosids" (The Journal of A rachutology, Vol. 30 , No. 3, pp. 571-587), we find that the carapace length of the adult male . mollicoma is normally distributed with mean and standard deviation .
a. Find the percentage of adult male . mollicoma that have carapace length between and .
b. Find the percentage of adult male . mollicoma that have carapace length cxcceding .
c. Determine and interpret the quartiles for carapace length of the adult male . mollicoma.
d. Obtain and interpret the percentile for carapace length of the adult male . mollicoma.
What do you think about this solution?
We value your feedback to improve our textbook solutions.