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A sample of n=18 observations is drawn from a normal population with μ=1040 and σ=230. Find...

A sample of n=18 observations is drawn from a normal population with μ=1040 and σ=230. Find each of the following:

A. P(X¯>1159)

Probability =

B. P(X¯<953)

Probability =

C. P(X¯>996)

Probability =

Solutions

Expert Solution

olution :

Given that,

mean = =1040

standard deviation = = 230

n = 18

= 1040

  =  ( /n) = (230 / 18 ) = 54.2115

A ) (    > 1159 )

= 1 - P ( < 1159)

= 1 - P ( - /)  <  (1159 - 1040 /54.2115)

= 1 - P( z  <  119 / 54.2115 )

= 1 - P ( z <  2.20 )   

Using z table

= 1 - 0.9861

= 0.0139

Probability = 0.0139

B ) ( < 953)

P ( - /)  <  (953 - 1040 /54.2115)

P( z  < - 87 / 54.2115 )

P ( z < -1.60 )   

Using z table

= 0.0548

Probability = 0.0548

C ) (    > 996 )

= 1 - P ( < 996)

= 1 - P ( - /)  <  ( 996 - 1040 /54.2115)

= 1 - P( z  < - 44 / 54.2115 )

= 1 - P ( z < - 0.81 )   

Using z table

= 1 - 0.2090

= 0.7910

Probability = 0.7910

milcah answered 8 months ago
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