Question

162-60-102 6. Total: 6 points. The weights of packages carried by UPS courier service has a normal distribution with a mean of 17.2 ounces and a standard deviation of 6.3 ounces. (3 peo) It is proposed that packages weighing over 24 ounces will be subjected to a surcharge. What proportion of packages will be affected by the surcharge? u=17.2 o=6.3 a P(x>24) = P(Z >24-17, 2) = P(Z >1.08) =.140 b. (3 pts) A random sample of 20 packages is taken. Find the probability that their average weight is between 15 and 18 ounces. n=20 < Z L 6.3/020 P(15<*218) IS- 17.2 18-17.2 6.3/020 = (-1.56 cz L. 57) = 12 c.57) IZ L-1.56) . F. 6563 normdcdfl-1.56,0.57)

Answer 1

6a. P(X> 24) = P( (X-17.2)/6.3 >(24-17.2)/6.3)=P(Z>1.08)=1-P(Z<1.08)=1-0.8599=0.1401

So the probability that the package is affected by surcharge is 0.1401

Hence, the proportion of package is thus 0.1401 that is affected by surcharge. (Ans)

6b.Since X~Normal(mean=17.2,SD=6.3)

The mean of X i.e Xbar ~Normal(mean=17.2,SD=6.3/√20) Since Xbar~Normal(µ,ơ/√n)

So, P(15<Xbar<18)=P( (15-17.2)/(6.3/√20) < Z < (18-17.2)/(6.3/√20))=P(-1.5616<Z<0.5679)

=P(Z<0.57)-P(Z<-1.56)=0.7157-0.0594=0.6563