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#### karush

##### Well-known member

- Jan 31, 2012

- 3,071

The heights of the girls are normally distributed with a mean $155$cm and a standard deviation of $10$cm

The heights of the boys are normally distributed with a mean $160$cm and a standard deviation of $12$cm

(a) Find the probability that a girl is taller than $170$cm.

$\frac{155-170}{10}=1.5$

so with $\mu=0$ and $\sigma=1$ then $P(x>1.5) =0.0668072$

View attachment 1090

(b) Given that $10\%$ of the girls are shorter than $x$cm, find $x$

from z-table $10\%$ is about $.25$ so $.25=\frac{x-155}{10} x\approx157$

but i don't think this is the answer $143$ looks closer so ????

there is still (c), (d), and (e) but have to do later