Answer in Statistics and Probability for Justine #88640
January 24th, 2023
If “Xsim N(mu,sigma^2)” then “Z=dfrac{X-mu}{sigma}sim N(0, 1)”
“mu=R50,000, sigma= R20,000”
a. What salary would an employee need to get in order to be in the lowest 30%?
“P(X<x^*)=P(Z<z^*)=0.3=>z^*=-0.5244”
“x^*=z^*sigma+mu”
“x^*=-0.5244(R20000)+R50000=R39512”
b. What is the probability of having an above average salary range of between R60000 to R80000
“z_1=dfrac{R60000-R50000}{R20000}=0.5”
“z_2=dfrac{R80000-R50000}{R20000}=1.5”
“P(R60000<X<R80000)=P(0.5<Z<1.5)=”
“=P(Z<1.5)-P(<Z<0.5)=0.93319280-0.69146246=”
“=0.24173034”
