Question

PLEASE HELP ME LEARN THIS

Answer 1

Birth weights in Norway are normally distributed with a mean of 3570 g and a standard deviation of 500 g. Find the probability that 100 randomly selected birth weights have a mean between 3500 g and 3600 g.

Answer 2

its the central limit theorem

Answer 3

if you know anyone who can help please tag them thanks :)

Answer 4

\(n=100\), \(\sigma_{\overline{x}}=\dfrac{\sigma}{\sqrt{n}}=\dfrac{500}{\sqrt{100}}=50\)
and \(\mu_{\overline{x}}=3570\)

You are asked to find \(P(3500<\overline{X}<3600)\) By standardizing:
\[Z=\frac{\bar{X}-\mu_{\overline{x}}}{\sigma/\sqrt{n}}\]

\(P(3500<\overline{X}<3600)=\left(\dfrac{3500-3570}{50}< \dfrac{\bar{X}-3750}{50}<\dfrac{3600-3570}{50}\right)\\
=P(-1.4<Z<0.6)\)

Answer 5

Then the rest should be easy.
\(P(-1.4<Z<0.6)=P(Z<0.6)-P(Z<-1.4)\)