Answer in Statistics and Probability for Adjanor Doris #120056
a) Let “X=” the height of the traveller:“Xsim N(mu, sigma^2).” Then “Z=dfrac{X-mu}{sigma}sim N(0,1)”
Given “mu=160 cm,sigma=8 cm”
(i)
“P(148<X<175)=P(X<175)-P(Xleq 148)=”“=P(Z<{175-160over 8})-P(Zleq{148-160over 8})=”“=P(Z<1.875)-P(Zleq-1.5)approx”“approx0.9696-0.0668=0.9028”
(ii)
“P(X>164)=1-P(Xleq 164)=1-P(Zleq{164-160over 8})=”
“=1-P(Zleq0.5)approx1-0.6915=0.3085”
(iii)
“P(X<179)=P(Z<{179-160over 8})=P(Z<2.375)approx”“approx0.9912”
b) Let “X=” the time taken for the nearest Covid-19 ambulance team to convey a patient:
“Xsim N(mu, sigma^2).” Then “Z=dfrac{X-mu}{sigma}sim N(0,1).”
Given “mu=60 s, sigma=8 s”
(i)
“P(X<50)=P(Z<{50-60over 8})=P(Z<-1.25)approx”“approx0.1056”
“200cdot0.1056approx21”
(ii)
“P(X>64)=1-P(Z<{64-60over 8})=1-P(Z<0.5)approx”“approx0.3085”
“0.3085cdot 200=62”
c) Let “X=” the Shelf life of a particular dairy product:“Xsim N(mu, sigma^2).”
Then “Z=dfrac{X-mu}{sigma}sim N(0,1).”
Given “mu=12, sigma^2=9”
“P(13<X<16)=P(X<16)-P(Xleq13)=”
“=P(Z<{16-12over 3})-P(Zleq{13-12over 3})approx”
“approx P(Z<1.3333)-P(Zleq0.3333)approx”
“approx0.9088-0.6306=0.2782”
About “27.82 %” of the products last between 13 and 16 days
