Question

10. For the population and sampling distributions corresponding to a and b above, calculate the following probabilities. The above a and b referenced are a. X ~ N (0,4) and b. X ~ N (15,7)

a. P(X > 1.5); P(X¯ > 1.5)

b. P(X < 8); P(X¯ < 8)

Answer 1

a)

µ =    0                  
σ =    2                  
                      
P ( X ≥   1.50   ) = P( (X-µ)/σ ≥ (1.5-0) / 2)              
= P(Z ≥   0.750   ) = P( Z <   -0.750   ) =    0.2266   (answer)

b)

µ =    15      
σ =    2.645751311      
          
P( X ≤    8   ) = P( (X-µ)/σ ≤ (8-15) /2.64575131106459)  
=P(Z ≤   -2.646   ) =   0.00408

Please revert in case of any doubt.

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