Question

1. True or False: If P(A) is the probability that an event A will occur, then 0< (or equal to) P(A) < (or equal to) 2.

2.True or False: If S represents the sample space of a random process, then P(S) =1

3. True or False: According toe the CLT, is a random variable X does not have a normal distribution in a population, the distribution of all sample means is approximately normal as long as the sample size is large enough.

4. True or False: The mean of the distribution of all sample means depends on the sample size.

5. True or False: For large sample sizes, the distribution of all sample means has a smaller spread than the population normal distribution.

6. True or False: If c represents a particular z-score and P(z>c) <0.5, then c is positive.

Answer 1

1. False . (0 ≤ P(A) ≤ 1 )

2. False . ( P(S)≠1 )

3. True (In central limit theorem (CLT) when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a bell curve) even if the original variables themselves are not normally distributed.

4. True. (sample mean =sum of samples/n)

5. True . ( The spread is smaller for larger samples, so the standard deviation of the sample means decreases as sample size increases.)

6. True.