This question is incomplete, the complete question is;
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?
Answer: 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
