Question

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) =

Answer #1

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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