**Mathematics Test Analysis for 8th-Grade Students in New York State**The scores on a standardized mathematics test for 8th-grade children in New York State follow a normal distribution. The distribution has a mean (μ) of 70 and a standard deviation (σ) of 10. **Question Analysis:**a. **Individual Scores:** - What proportion of the students in the state have scores less than X = 75?b. **Sample Means (n = 4):** - If samples of size n = 4 are selected from the population, what proportion of the sample means will be less than M = 75?c. **Sample Means (n = 25):** - If samples of size n = 25 are selected from the population, what proportion of the sample means will be less than M = 75?This analysis involves understanding the properties of normal distribution and calculating proportions using the standard normal distribution (z-scores). The calculations differ slightly for individual scores versus sample means due to the application of the Central Limit Theorem.

Answered: Image /qna-images/answer/54c0c331-c09d-4cb9-bde6-6c74ce62a5c3.jpg

Answered: 4. The scores on a standardized…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1.In a certain wildlife reserve the life span of monkey are normally distributed. The average monkey lives 20.8 years and The standard deviation is 3.1 years. Use the empirical rule to estimate the probability or percentage of a monkey living less than 23.9 years. 2. If the population of the monkey are 568, how many of them will live for less than 23.9 years. 3. IQ scores which are normallu distributed have a mean of 100 and a standard deviation of 16. The z score that corresponds to Albert IQ Is 3.75. What is his IQ?
2. The population standard deviation for the age of Fictional College students is 8.4 years. If we want to be 95% confident that the sample mean age is within one year of the true population mean age of Fictional College students, how many randomly selected Fictional College students must be surveyed?
1. An experimenter feels that a population standard deviation is no larger than 17.0and would like to construct a 95% two-sided t-interval for the population mean that has alength at most 2.8. What sample size would you recommend?
III
Suppose that in 2020 the average song length is 245 seconds, with a standard deviation of 28 seconds. what is the approximate standard error for the sampling distribution of mean song lengths due samples size of 64 A. 28.0 B. 2.3 C. 7.0 d. 3.5
4. You ask an SRS of 1500 college students whether they applied for admission to any other college. Suppose that in fact 35% of all college students applied to colleges besides the one they are attending. The sampling distribution of the proportion of B your sample who say "Yes" is approximately Normal with mean 0.35 and standard deviation 0.01. Sketch this Normal curve and use it to answer the following questions. (You can use the 68-95-99.7 rule for all these questions.) Round to nearest whole percent. (a) What percentage of many samples would have a larger than 0.37? 2.5 (b) What is the probability that your sample will have a less than 0.33?Å (c) what is the probability that your sample result will be either less than 0.33 or greater than 0.35?
A previous study found that the students' scores in a national examination in 2020 are normally distributed with mean 74 and standard deviation 3.5. a. What percentage of students got a score of at least 80? b. Given the total number of examinees is 2500, how many got a score of at least 80?
2. Ms. Palac, a sociologist, made a study on the age in years of a woman at the time of her first marriage. She randomly selected a sample of 24 and 21 married women from Village A and Village B, respectively. The following data are the mean and standard deviation for each group: Village A: x = 18.63 and s = 5.54 Village B: x = 24.90 and s = 5.54 Test the hypothesis that the women in Village A get married younger than women in Village B. Use 0.10 significance level. Step 1: Null and Alternative Hypothesis Ho: Ha: Step 2: Level of Significance and appropriate test statistic Step 3: Determine the Critical Region Degrees of Freedom (df): Critical Region: Step 4: Compute the z or t value Computations: Step 5: Decide whether to accept or reject Ho Step 6: Conclusion
4. You want to estimate the mean weight loss of people one year after using the Atkins diet. How many dieters must be surveyed if we want to be 95% confident that the sample mean weight loss is within 0.20 lb of the true population mean? Assume that the population standard deviation is known to be 10.8 lb.

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