Answer to Question #142605 in Statistics and Probability for Jonel

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

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

$\sigma=5.294$