Answer to Question #217985 in Statistics and Probability for Kaypoms

Question

The weekly wages of employees of volta gold normally distributed about a mean of $1250 with a standard deviation of $120. Find the probability of an employee having a weekly weekly wage lying. I. Between $1,320 and $970. ii. Under $1,400. iii. Over $1,290

Answer 1

$\mu=1250 \\ \sigma=120 \\ i. \; P(970<X<1320) = P(X<1320) -P(X<970) \\ = P(Z< \frac{1320-1250}{120}) -P(Z< \frac{970-1250}{120}) \\ = P(Z< 0.5833) -P(Z< -2.333) \\ = 0.72005-0.00982 \\ = 0.71023 \\ ii. \;P(X<1400) = P(Z< \frac{1400-1250}{120}) \\ =P(Z< 1.25) \\ = 0.8943 \\ iii. \; P(X>1290) = 1 -P(X<1290) \\ = 1 -P(Z< \frac{1290-1250}{120}) \\ = 1 -P(Z<0.3333) \\ = 1 -0.63043 \\ = 0.36957$