What is the probability a sample of 66 test takers will provide a sample mean test score within 10 points of the population mean of 533 on the Evidence-based Reading and Writing part of the test?

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A certain organization reported the following scores for two parts of the scholastic Aptitude test ( SAT)

Evidence-based Reading and writing  : 533

Mathematics                                           : 527

Assume the population standard deviation for each part is σ = 100.

What is the probability a sample of 66 test takers will provide a sample mean test score within 10 points of the population mean of 533 on the Evidence-based Reading and Writing part of the test?

the required probability is 0.582

Step-by-step explanation:

Given that;

Population mean = 533

sample size n = 66

population standard deviation σ = 100

σ of x bar = 100/√66 = 12.3091

Normal distribution with mean 533 and SD of 12.3091

P( 523 <x< 543 )

Z = 10 / 12.3091

Z = 0.8124, -0.8124

P( z < 0 0.8124) - P( z < -0.8124)      { from table}

⇒  0.7910 - 0.2090

= 0.582

Therefore, the required probability is 0.582

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Step-by-step explanation: