Question

Find the mean and the standard deviation of the heights of male engineering students in which the heights 66 inches and 75 inches correspond to standard score of -0.6 and 1.1, respectively.

Answer 1

$\frac{66-\mu}{\sigma}=-0.6$ and

$\frac{75-\mu}{\sigma}=1.1$

From the first equation $\frac{-(66-\mu)}{0.6}=\sigma$

$\frac{75-\mu}{\frac{-(66-\mu)}{0.6}}=1.1$

${75-\mu}=1.1(\frac{-(66-\mu)}{0.6})$

$45-0.6\mu=1.1\mu-72.6$

$45+72.6=1.7\mu$

$\mu=\frac{117.6}{1.7}=$ 69.176

$\frac{-(66-69.176)}{0.6}=\sigma$

$\sigma=5.294$