Question

Chance (Fall 2004) published a study on modeling a certain pitch of a musical composition. Data on 147 famous compositions were used to model the numb

Modeling
ANSWERED
asked 2021-05-31

Chance (Fall 2004) published a study on modeling a certain pitch of a musical composition. Data on 147 famous compositions were used to model the number of times (y) a certain pitch occurs called entropy- as a straight-line function of year of birth (x) of the composer. On the basis of the scatterplot of the data, the standard deviation \(\sigma \sigma\) of the model is estimated to be \(s = .1\). For a given year (x), about 95% of the actual entropy values (y) will fall within d units of their predicted values. Find the value of d.

Answers (1)

2021-06-01

Given: \(s=1\)
The Empirical Rule or (68-95-99.7 rule) tells us: Approximately 68% of the observations are within 1 standard deviation of the mean.
Approximately 95% of the observations are within 2 standard deviations of the mean.
Approximately 99.7% of the observations are within 3 standard deviations of the mean.
By the empirical rule, about 95% of the data. values are within two standard deviations of the mean.
About 95% of the actual y-values are within 2s of the predicted y-values (due to the fact that the errors have approximately a, normal distribution with standard deviation s).
\(d=2 s=2(0.1)=0.2\)

0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-06-06

Colleen and Martin are modeling the data shown. Colleen thinks the model should be \(\displaystyle{f{{\left({x}\right)}}}={5.754}^{{x}}{3}+{2.912}{x}^{{2}}−{7.516}{x}{0.349}\). Martin thinks it should be \(\displaystyle{f{{\left({x}\right)}}}={3.697}{x}^{{2}}+{11.734}{x}−{2.476}\). Is either of them correct? Explain your reasoning.
f(x) -2-190.5-2 -1511.5 00.4243

asked 2021-06-07
Global warming is a topic of concern and of political discussion. Without doing research, discuss how modeling might be used to determine what might be done to reduce global warming.
asked 2021-06-29

Identify each function as modeling either exponential growth or exponential decay. What percent of increase or decrease does the function model? \(\displaystyle{y}={0.1}{\left({1.7}\right)}^{{x}}\)

asked 2021-06-02

Identify each function as modeling either exponential growth or exponential decay. What percent of increase or decrease does the function model? \(y=7.3(0.8)^x\)

asked 2021-05-07
The following question consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells. [T] The Gompertz equation has been used to model tumor growth in the human body. Starting from one tumor cell on day 1 and assuming α=0.1α=0.1 and a carrying capacity of 10 million cells, how long does it take to reach “detection” stage at 5 million cells?
asked 2021-06-19
When two targets are presented close together in a rapid visual stream, the second target is often missed. Psychologists call this phenomenon the attentional blink (AB). A study published in Advances in Cognitive Psychology (July 2013) investigated whether simultaneous or preceding sounds could reduce AB. Twenty subjects were presented a rapid visual stream of symbols and letters on a computer screen and asked to identify the first and second letters (the targets). After several trials, the subject's AB magnitude was measured as the difference between the percentages of first target and second target letters correctly identified. Each subject performed the task under each of three conditions. In the Simultaneous condition, a sound (tone) was presented simultaneously with the second target; in the Alert condition, a sound was presented prior to the coming of the second target; and in the No-Tone condition, no sound was presented with the second target. Scatterplots of AB magnitude for each possible pair of conditions are shown below as well as the least squares line for each. a. Which pair of conditions produces the least squares line with the steepest estimated slope? b. Which pair of conditions produces the least squares line with the largest SSE? c. Which pair of conditions produces the least squares line with the smallest estímate of σ?
asked 2021-05-03

Identify each function as modeling either exponential growth or exponential decay. What percent of increase or decrease does the function model? \(y=0.32(0.99)^x\)

asked 2021-02-11

Determine the algebraic modeling which of the following data sets are linear and which are exponential. For the linear sets, determine the slope. For the exponential sets, determine the growth factor or the decay factor
a) \(\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & \frac{1}{9} & \frac{1}{3} & 1 & 3 & 9 & 27 & 81 \\ \hline \end{array}\)

b) \(\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 2 & 2.6 & 3.2 & 3.8 & 4.4 & 5.0 & 5.6 \\ \hline \end{array}\)

c) \(\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 3.00 & 5.0 & 7 & 9 & 11 & 13 & 15 \\ \hline \end{array}\)

d) \(\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 5.25 & 2.1 & 0.84 & 0.336 & 0.1344 & 0.5376 & 0.021504 \\ \hline \end{array}\)

asked 2021-06-06
Use the strategy for solving word problems modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and 88. There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than 80, you will lose your B in the course. Describe the grades on the final that will cause this to happen.
asked 2021-06-23
Use the strategy for solving word problems modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and 88. There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90. What must you get on the final to earn an A in the course?

You might be interested in

...