E)Use the empirical rule to approximate the percentage of people who take the SAT that will have a mathematics SAT score at least 397. ---### Understanding SAT Mathematics Scores with the Empirical RuleThe mean mathematics SAT score for all people who took the SAT in a particular year was 514 with a standard deviation of 117. Assume the mathematics SAT score is normally distributed.#### a) Identifying Components:**Individual, Variable, and Type of Variable:**- **The individual** is a randomly selected person who took the SAT.- **The variable** collected from each individual is the mathematics SAT score.- **This variable** is a quantitative -- discrete variable.#### b) Definition of Random Variable X:**Random Variable X:**- The random variable X = the mathematics SAT score of a randomly selected person who took the SAT.#### c) Application of Empirical Rule:**Empirical Rule Application:**- The Empirical Rule can only be used to approximate probabilities for problems where the random variable has a normal distribution. Since the mathematics SAT score is normally distributed, the Empirical Rule is applicable here.#### d) Calculating Probabilities using Empirical Rule:**Percentage of People Scoring Between 163 and 631:**- There is about 83.85% of people who take the SAT that will have a mathematics SAT score between 163 and 631.#### e) Percentage of People Scoring At Least 397:**Percentage of People Scoring At Least 397:**- There is about 34% of people who take the SAT that will have a mathematics SAT score of at least 397. Note that this part contained a mistake as the correct percentage should be analyzed and corrected according to the accurate use of the Empirical Rule.*Note: The Empirical Rule states that approximately 68% of data within one standard deviation (±1σ), 95% within two (±2σ), and 99.7% within three (±3σ).*---This exercise demonstrates the proper use of statistical tools and methods for analyzing normally distributed data, essential in various educational assessments and research.

It is given that Mean, μ = 514Standard deviation, σ = 117

e) Use the Empirical Rule to approximate the percentage of people who take the SAT that will I have a mathematics SAT score of at least 397? • There is about 34 score of a least 397. X% of people who take the SAT that will have a mathematics SAT

e) Use the Empirical Rule to approximate the percentage of people who take the SAT that will I have a mathematics SAT score of at least 397? • There is about 34 score of a least 397. X% of people who take the SAT that will have a mathematics SAT

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514. SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree. College Grads 485 487 518 517 650 542 570 426 566 499 588 562 497 448 592 453 High School Grads 442 492 580 478 479 425 486 485 528 390 524 535 (b) What is the point estimate of the difference between the means for the two populations? (c) Find the value of the test statistic. (Round your answer…
) In the recent study, US graduates of for-profit higher institutions were between 4.8 and 6.7 percentage points more likely to ne unemployed than those at nonprofit institutions and community colleges. Determine the population, the sample, and population parameter of sample statistic. B) Explain the difference between Amelia making an 82 on her pre-calculus exam and scoring in the 82nd percentile in mathematics on the ACT test.
UBS Wealth Management UK periodically ask their customers to evaluate their financial consultants and services. The higher the customer rating, the better the perceived service. The maximum rating is 7. Independent samples of two financial consultants are given below. Consultant A has 10 years' experience, Consultant B has 1 years' experience. Use α = 0.05 and test to see whether the consultant with more experience has the higher population mean service rating. Consultant A Consultant B N1 = 16 N2 = 10 Mean1 = 6.82 Mean2 = 6.25 S1= 0.64 S2 = 0.75 State the null and alternative hypothesis, Compute the value of the test statistic. What is the p-value? What is your conclusion?
The city council is considering a law that would ban smoking in all public facilities. A sample has been selected from the community and tested for support of the ordinance. Is there a statistically significant relationship between age and support for the anti-smoking law? Use the five step model as a guide and write a sentence or two interpreting your results. Age Less than 40 More than 40 Support: For 145 78 223 Against 103 169 272 248 247 495
The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of 52 records of automobile driver fatalities in a certain county showed that 35 involved an intoxicated driver. Do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County? Use ? = 0.10. What is the value of the sample test statistic? (Round your answer to two decimal places.)=__ (c)Find the P-value of the test statistic. (Round your answer to four decimal places.)=__
please do the following parts, this is one question! hypotheses, assumptions, and please check the assumptions (listed as a problem in the image)
The answer should be step by step and the answer should be no plagiarism.
Q3.3 Normal, but why? A meal package for use at the space station is to be prepared by combining three separate components: protein, fruit/vegetable, and grains. Each of the components is to be randomly selected. Summary values for the caloric content for each of the components are given in the table. Component Protein (P) Fruit/vegetable (F) Grain (G) Mean (calories) 120 55 84 Stdv (calories) 6.4 Save Answer 1.0 3.6 Assume that the distributions of caloric content for each of the components are approximately normally distributed. Since the meal package consists of protein, fruit/vegetable, and grains, the total caloric content of a meal package is the random variable T, where T = P + F + G. Briefly explain why it is appropriate to say that T is approximately normally distributed. Q3.4 Probability Less than 275 Calories On your own piece of paper find the approximate probability that a randomly selected meal package will have less than 269 calories? (Draw an appropriate diagram, find a…
Can someone please answer d.) e.) and f.)
The average home in the US is expected to cost $240,000. A random sample of 56 homes sold this month showed average price of $232,000. Assume you have access to this data. We are interested in determining cost if the cost of average home has decreased this month. If the test statistic is -1.66 what is the p-value?
A company that has a 10% market share (they sell their product to 10% of all potential buyers) launches a marketing campaign. At the end of the campaign period, the company conducts a survey in order to assess whether its market share has increased. The result of the survey issued to 500 customers was 12.5%.h0= p=0.10, h1= p>0.10test statistic= 1.86P value= 0.0314 a. State your conclusion using ΅ = 0.05.b. What would be the potential Type I and Type II errors in this problem? Explain these possible errors in context.
1.) Write your solution A. Determine the 1" quartile, 2 quartile, 3rd quartile and interquartile range (IQR), given the scores of; 11, 24, 23, 11, 13, 17, 15, 19, 21, then interpret each of your answer. B. Solve for the Percentile Rank of 17.