Answer to Question #118748 in Statistics and Probability for Tanya

Question

In a WAITS, one subtest the raw score has a mean of 55 and variance of 25. What is the probability of obtaining a raw score between the mean and 46? AND between 50 and 58?

Answer 1

$Given \; that, μ=55, σ^{2}=25, σ=5,then,\\ a) P(46<x<55) = P(\frac{46-55}{5}< Z <\frac{55-55}{5})\\ =P(-1.8<Z<0)\\= P(0<Z<1.8)=0.4641\\ b) P(50<x<58) = P(\frac{50-55}{5}< Z <\frac{58-55}{5})\\ =P(-1<Z<0.6)\\ = P(0<Z<1)+ P(0<Z<0.6)\\ =0.3413+0.2257=0.567$