Question

# Suppose a simple random sample of size n=39 is obtained from a population with μ=6666 and...

Suppose a simple random sample of size n=39 is obtained from a population with μ=6666 and σ=14.

P(x overbar < 69.2) =

P(x overbear great than or equal to 67.8) =

a)

X ~ N ( µ = 66 , σ = 14 )
P ( X < 69.2 )
Standardizing the value
Z = ( X - µ ) / (σ/√(n)
Z = ( 69.2 - 66 ) / ( 14 / √39 )
Z = 1.43
P ( ( X - µ ) / ( σ/√(n)) = ( 69.2 - 66 ) / ( 14 / √(39) )
P ( X < 69.2 ) = P ( Z < 1.43 )
= 0.9236

b)

X ~ N ( µ = 66 , σ = 14 )
P ( X >= 67.8 ) = 1 - P ( X < 67.8 )
Standardizing the value
Z = ( X - µ ) / ( σ / √(n))
Z = ( 67.8 - 66 ) / ( 14 / √ ( 39 ) )
Z = 0.8
P ( ( X - µ ) / ( σ / √ (n)) > ( 67.8 - 66 ) / ( 14 / √(39) )
P ( Z > 0.8 )
P ( X̅ >= 67.8 ) = 1 - P ( Z < 0.8 )
= 1 - 0.7881
= 0.2119

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