Question

Find the area of the shaded region. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
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Answer 1

solution

given : mean = 100 standard deviation = 15

z score = (X - mean )/ standard deviation : let X is a random variable

the area of the shaded region = P( 95 < X <125 ) =

=P( {95 - mean }/standard deviation < {X - mean }/standard deviation < {125 - mean }/standard deviation )

=P( -0.33 < z < 1.67)

= P(0< z< 1.67) + P(0 <z <0.33)

= 0.4525 + 0.1293 { from area of normal probabilty curve(table)}

=0.5818

so,the area of the shaded region= 0.5818