Question #26011

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Answer 1 · 2017-04-27T19:01:06

$P (X < 127) = 0.9641 .$ $P(X<127)=0.9641.$

If $X = RV the IQ of an adult$ $X="RV the IQ of an adult "$

we have

$X ~ N (100, 15^{2})$ $X~N(100,15^2)$

and require to find

$P (X < 127)$ $P(X<127)$

we need to change the $X$ $" "X" "$ variable we to the standard $Z$ $Z" "$ variable for a Normal distribution using the standardising formula

$Z = \frac{X - μ}{σ}$ $Z=(X-mu)/sigma$

$P (Z < \frac{127 - 100}{15}) = P (Z < 1.8)$ $P(Z<(127-100)/15)=P(Z<1.8)$

we now use the standard Normal tables to find this probability

=0.9641

Thus

$P (X < 127) = 0.9641 .$ $P(X<127)=0.9641.$