5. Assume that you have a binomial experiment with $p = 0.5$ and a sample size of 100. The expected value of this distribution is
(A) 0.50
(B) 0.30
(C) 100
(D) 50
(E) 25

6. A standard normal distribution is a normal distribution (A) With a mean of 1 and a standard deviation of 0 (B) With a mean of 0 and a standard deviation of 1 (C) With any mean and a standard deviation of 1 (D) With any mean and any standard deviation (E) With a mean of 0 and a standard deviation of 0

7. The probability distribution of random variable, Xᵢ is defined as follows: What is the missing value? (A) 0 (B) 0.1 (C) 0.2 (D) 0.3 (E) 0.4

8. A box contains 10 bulbs, 2 of which are defective. If 3 bulbs are picked randomly, what is the probability that at least one defective is picked? (A) \( \frac{1}{6} \) (B) \( \frac{8}{15} \) (C) \( \frac{2}{3} \) (D) \( \frac{7}{15} \) (E) \( \frac{5}{6} \)

9. Independently toss a fair dice 4 times. Suppose that Xᵢ is the outcome of the iᵘ toss, and X̄ = (X₁ + X₂ + X₃ + X₄) / 4. Then Var(X̄) is: (A) \( \frac{35}{12} \) (B) \( \frac{35}{24} \) (C) \( \frac{35}{36} \) (D) \( \frac{35}{48} \) (E) \( \frac{35}{60} \)

10. As the sample size increases, the (A) Standard deviation of the population decreases (B) Population mean increases (C) Sample mean increases (D) Standard error of the sample mean increases (E) Standard error of the sample mean decreases

11. A random sample of size 25 is to be taken from a population that is normally distributed with mean 60 and standard deviation 10. The average $\overline{x}$ of the observations in our sample is to be computed. The sampling distribution of $\overline{x}$ is (A) Normal with mean 60 and standard deviation 10 (B) Normal with mean 60 and standard deviation 2 (C) Normal with mean 60 and standard deviation 0.4 (D) Normal with mean 60 and standard deviation 25 (E) Normal with mean 60 and standard deviation 2.5

12. The SAT scores of entering freshmen at a certain university have mean 1215 and standard deviation 110. A random sample of 100 freshmen is taken and $\overline{x}$, the sample mean of their SAT scores, is computed. The probability that $\overline{x}$ less than 1190 is (A) 0.0116 (B) 0.1335 (C) 0.4090 (D) 0.4562 (E) 0.1628

13. As the sample size becomes larger, the sampling distribution of the sample mean approaches a (A) Binomial distribution (B) Poisson distribution (C) Normal distribution (D) Chi-square distribution (E) t distribution

14. Which of the following is true? (A) If we draw a simple random sample of any size from any population the sampling distribution of the sample mean will be exactly Normal. (B) If we draw a simple random sample of any size from any population the sampling distribution of the sample mean will be close to Normal. (C) Central limit theorem only applies when sampling from Normal populations. (D) None of the above.

15. A professor of statistics refutes the claim that the average student spends 3 hours studying for the midterm exam. The professor thinks the students spend more time than that. Which hypotheses are used to test the claim? (A) \( H_0: \mu \leq 3 \) vs. \( H_a: \mu > 3 \) (B) \( H_0: \mu = 3 \) vs. \( H_a: \mu \neq 3 \) (C) \( H_0: \mu \neq 3 \) vs. \( H_a: \mu = 3 \) (D) \( H_0: \mu = 3 \) vs. \( H_a: \mu < 3 \) (E) \( H_0: \mu \geq 3 \) vs. \( H_a: \mu = 3 \)

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