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?
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
Among all the applicants to the ABC university in one year, the sat scores followed a...
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