Question

Suppose that the mean weight of school children’s bookbags is 17.41 pounds, with a standard deviation of 2.2 pounds. Find the probability that the mean weight of a sample of 30 bookbags will exceed 17 pounds.

Answer 1

Set the weights of school children's book bags as variable x.

Given: $x\thicksim N(17.41,2.2^2)$

$n(x)=30$

Get: $\mu_{\=x}=\mu_x=17.41,$ $\sigma_{\=x}^2=\frac{\sigma_x^2}{n}=\frac{2.2^2}{30}=(\frac{2.2}{\sqrt{30}})^2$

$\=x\thicksim N(17.41,(\frac{2.2}{\sqrt{30}})^2)$

$P(\=x>17)=1-P(\=x\le17)\\ =1-P(\frac{\=x -17.41}{\frac{2.2}{\sqrt{30}}}\le\frac {17-17.41}{\frac{2.2}{\sqrt{30}}})\\ =1-P(z\le-1.02)=1-Z(-1.02)\\ =1-[1-Z(1.02)]=Z(1.02)\\ =0.8461$

(using z-score table)