1. Describe the probability distribution of $\displaystyle {X}$ and state its parameters $\displaystyle \mu$ and $\displaystyle \sigma$:

 $\displaystyle {X}\sim$ Select an answer T B F N ? χ² ( $\displaystyle \mu=$ , $\displaystyle \sigma=$ )

and find the probability that the ACT score of a randomly selected student is more than 34 points.

(Round the answer to 4 decimal places)

2. Use the Central Limit Theorem

Select an answer the sample size is small (n<30) and the distribution of the original population is unknown the original population is normally distributed and the sample is large (n>30) the sample size is large (n>30) although the distribution of the original populaiton is unknown the original population is normally distributed although the sample size is small (n<30)

to describe the probability distribution of $\displaystyle \overline{{{X}}}$ and state its parameters $\displaystyle \mu_{\overline{{{X}}}}$ and $\displaystyle \sigma_{\overline{{{X}}}}$: (Round the answers to 1 decimal place)

 $\displaystyle \overline{{{X}}}\sim$ Select an answer ? F N χ² B T ( $\displaystyle \mu_{\overline{{{X}}}}=$ , $\displaystyle \sigma_{\overline{{{X}}}}=$ )

and find the probability that the average ACT score of a sample of 10 randomly selected students is more than 25 points.

(Round the answer to 4 decimal places)