Statistics. Please check my answers.?

3-22


Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy adults, x is approximately normally distributed with mean µ = 38 and standard deviation σ = 12. What is the probability that


(a) x is less than 60?


x %26lt; 60


P( ( x - μ ) / σ %26lt; ( 60 - 38 ) / 12 )


= 1.83


= P( z %26lt; 1.83)


= 0.9664


= 97%





(b) x is greater than 16?


16 %26lt; x


P( ( x - μ ) / σ %26gt; ( 16 - 38 ) / 12)


= P( z %26gt; -1.83 )


= P( z %26lt; 1.83 )


= 0.9664


= 97%





(c) x is between 16 and 60?


16 %26lt; x %26lt; 60


P( (16 - 38 ) / 12 %26lt; ( x - μ ) / σ %26lt; (60 - 38 ) / 12 )


= P(-1.83 %26lt; z %26lt; 1.83 )


= P( z %26lt; 1.83 ) - P( z %26lt; 1.83 )


= 0.9664 - 0.9664


= 0


= 0.5000


= 50%





(d) x is more than 60?


60 %26lt; x


P( ( x - μ ) / σ %26gt; ( 60 - 38 ) / 12)


= P( z %26gt; 1.83 )


= P( z %26lt; -1.83 )


= 0.0336


= 3%

Statistics. Please check my answers.?
(a), (b), (d) are correct


(c) Z = (16-38)/12 = -1.83


Φ[-1.83] = 0.0336


Z = (60-38)/12 = 1.83


Φ[1.83] = 0.9664


Then 0.9664-0.0336 = 0.933

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