Calculating SAT Score Probability: Sample Mean vs Population Mean

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Homework Help Overview

The discussion revolves around calculating probabilities related to sample means in statistics, specifically in the context of SAT scores. The original poster presents a problem involving the population mean and standard deviation, seeking assistance with probability calculations for sample means based on given criteria.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the standard deviation in relation to the sample size and how to apply it to find probabilities. Questions arise about the interpretation of "within" a certain range of the population mean and how to correctly calculate probabilities using the z-distribution.

Discussion Status

There is an ongoing exploration of how to approach the problem, with some participants clarifying the need to consider both directions (above and below the mean) when calculating probabilities. Guidance has been offered regarding the interpretation of the problem, but no consensus has been reached on the exact method to use.

Contextual Notes

Participants are working under the constraints of a homework assignment with a deadline, which adds urgency to their discussions. There is also a focus on understanding the statistical concepts involved, such as the normal distribution and the calculation of standard deviations from sample sizes.

yeungmei
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Please please help me, i totally forgot about Stat and now i have a question due tomm.

The College Board American College Testing Progam reproted a population mean SAT score of U=1020. Assume that the population standard deviation is O-100

a) what is the probability that a random sample of 75 students will provide a sample mean SAT score within 10 of the population mean?

b) what is the probability a random sample of 75 students will provide a sample mean SAT score within 20 of the population mean?

Please please help !
 
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Do you know how to extract information from a z (normal distribution) chart?
 
I know u-1020 is the average also the centre point of a curve, where i should get o-100 devidied by square root of 75 to find the standard deviation.

so for a, should i uses 10 / the calculated SD to find the probability?
 
within 10 implies 10 points above or below the mean, so you would need to double any amount you found for the probability of finding the sample mean within 10 of the population mean from one side
 
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I thought it said within, so is it just use 10/SD to find?
 
10/SD isn't within, that's one direction (up OR down, not both)
 
Got it..Thanks ^__^
 

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