Question

Assume scores on a Biology exam are normally distributed, with a mean of 74 points and a standard deviation of 5.8 points. What is the probability that 40 randomly selected scores have a mean between 72 and 75?

Answer 1

\[\begin{align*}
P(72<X<75)&=P\left(\frac{72-74}{5.8}<\frac{X-74}{5.8}<\frac{75-74}{5.8}\right)\\\\
&=P(-0.345<Z<0.172)\\\\
&=P(Z<0.172) - P(Z<-0.345)
\end{align*}\]