Question

25 SAT scores are randomly selected from a population of SAT scores that are normally distributed. The population has a mean of 1518 and standard deviation of 325. What is the probability that the selected 25 scores have a mean between 1550 and 1575?

Answer 1

\[\begin{align*}P(1550<X<1575)&=P\left(\frac{1550-1518}{\frac{325}{\sqrt{25}}}<\frac{X-1518}{\frac{325}{\sqrt{25}}}<\frac{1575-1518}{\frac{325}{\sqrt{25}}}\right)\\\\
&=P(0.4923<T<0.8769)
\end{align*}\]
where \(T\) follows the \(t\) distribution with 24 degrees of freedom.