Among all the applicants to the ABC university in one year, the sat scores followed a...
Among all the applicants to the ABC university in one year, the sat scores followed a normal distribution with a mean of 550 and a standard deviation of 90.
Whats the probability that the average sat score among 20 randomly selected applicants is below 600?
Homework Answers
X ~ N ( µ = 550 , σ = 90 )
P ( X̅ < 600 )
Standardizing the value
Z = ( X - µ ) / (σ/√(n)
Z = ( 600 - 550 ) / ( 90 / √20 )
Z = 2.4845
P ( ( X - µ ) / ( σ/√(n)) < ( 600 - 550 ) / ( 90 / √(20) )
P ( X̅ < 600 ) = P ( Z < 2.48 )
P ( X̅ < 600 ) = 0.9935
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