The likelihood or probability that the population mean evidence-based reading and writing test score of 533 will be within 10 points of the sample mean test score provided by a sample of 49 test takers is 0.274.
From the given information, we have:
The population mean, μ = 533
The sample size, n = 49
The population standard deviation, σ = 100
The standard deviation for X is:
= 100/√49 = 14.2857142857
Normal distribution with mean 533 and SD of 12.3091
P( 523 <x< 543 )
Z = 10 ÷ 14.2857142857
Z = 0.7, - 0.7
P( z < 0.7 ) - P( z < - 0.7 )
= 0.75804 - 0.48393
= 0.27411
The required probability is 0.274.
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The complete question is mentioned below:
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 49 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?
