Answer in Statistics and Probability for wyatt #98389
January 24th, 2023
a) Given that “mu=15 years, sigma=2.3 years”
“Xsim N(mu, sigma^2)”
“Xsim(15, 2.3^2)”
b) “Xsim N(mu, sigma^2).” Then
“Z={X-mu over sigma}sim N(0, 1)”
“mu=15 years, sigma=2.3 years”
“P(13.9<X<16.1)=P(X<16.1)-P(X<13.9)=”
“=P(Z<{16.1-15 over 2.3})-P(Z<{13.9-15 over 2.3})approx”
“approx0.683768-0.316232approx0.3675”
“P(13.9<X<16.1)=0.3675”
c)
“P(mu-delta<X<mu+delta)=0.2”
“P(Z<{mu+delta-mu over sigma})-P(Z<{mu-delta-mu over sigma})=0.2”
“P(Z<{delta over sigma})-P(Z<-{delta over sigma})=0.2”
“P(Z<-{delta over sigma})={1-0.2 over 2}=0.4”
“-{delta over sigma}approx-0.253348”
“deltaapprox2.3cdot0.253348=0.5827004”
“mu-deltaapprox15-0.5827004approx14.4173”
“mu+deltaapprox15+0.5827004approx15.5827”
“Low:14.4173 years”
“High:15.5827 years”
