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4. The scores on a standardized mathematics test for 8th-grade children in New York State form a normal distribution with a mean of u = 70 and a standard deviation of o = 10. a. What proportion of the students in the state have scores less than X = 75? b. If samples of n = 4 are selected from the popula- tion, what proportion of the samples will have means less than M 75? c. If samples of n = 25 are selected from the popu- lation, what proportion of the samples will have means less than M 75? ||

4. The scores on a standardized mathematics test for 8th-grade children in New York State form a normal distribution with a mean of u = 70 and a standard deviation of o = 10. a. What proportion of the students in the state have scores less than X = 75? b. If samples of n = 4 are selected from the popula- tion, what proportion of the samples will have means less than M 75? c. If samples of n = 25 are selected from the popu- lation, what proportion of the samples will have means less than M 75? ||

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**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.
Transcribed Image Text:**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.
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