Answer to Question #143127 in Statistics and Probability for iverson

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 scores of -0.6 and 1.1 respectively

Answer 1

$Given \;that,\\ y_{1}=66,y_{2}=75,Z_{1}=-0.6,Z_{2}=1.1,then\\ Z=\frac{y-\mu}{\sigma}\\ \therefore -0.6=\frac{66-\mu}{\sigma}\implies -0.6\sigma=66-\mu,\\ \therefore 1.1=\frac{75-\mu}{\sigma}\implies 1.1\sigma=75-\mu,\\ \text{by multiplying the first equation by (-1) }\\ \text{and then adding the result to the second equation}\\ 1.7 \sigma=-66+75=9\implies \sigma=\frac{9}{1.7}\approx 5.294,\\ \mu=66+0.6(5.294)=69.1764\\$