Challenge yourself with these challenging questions. Only correct answers and explanations are needed.

1. Determine and state the central limit theorem.

2. Physic students decided to conduct an experiment that required an understanding of Weibull distribution. 2000 hours was the time to failure while shape of the bulb was . Determine the probability of the bulb lasting more than 4000 hours and the mean time to failure.

3. Define the term used to refer to the clusters that are selected from a clustering sample.

4. Given a population that contains 8 items, determine the number of the possible outcomes given that a random selection is conducted where only 2 items are selected without replacement.

5. Eight students were chosen out of the total 56 students in a class, determine the fraction of the sample of the students.

6. Determine the value of bias in sampling for sampling distribution where E(X)=11 and =13.

7. Given the F- distribution containing v1=5 and v2=9, solve for the variance.

8. There are 5 green, 15 blue, 8 red and 12 orange balls in a kindergarten. Given that each color occurs with equal frequency, test for the null hypothesis. What is the value of chi square?

9. What does the symbol p represent when conducting a hypothesis test. Expound on you answer.

10. Determine the assumption made during the performance of a hypothesis test using the T- distribution.