Assessment
Answer the following questions by writing the letter of the correct answer from the
choices below.
1. Which of the following does NOT illustrate the Central Limit Theorem?
A. The Central Limit Theorem is used to approximate the distribution of the
sample means over the population means.
B. If the sample size n, where n is sufficiently large is drawn from any population
with mean i and a standard deviation o, then the sampling distribution of
sample means approximates the normal distribution.
C. Whenever the population is not normally distributed, or if we do not know of
its distribution, the Central Limit Theorem allows us to conclude that the
distribution of sample means will be normal if the sample size is sufficiently
large.
D. Given a random variable X with mean y and variance o?, then regardless of
whether the population distribution of X is normally distributed or not, the
shape of the distribution of the sample means taken from the population
approaches a normal distribution.
2. The Central Limit Theorem states that:
A. the sample size is large.
B. all possible samples are selected.
C. the standard error of the sampling distribution is small.
D. the standard deviation is sufficiently large than the normal.
3. The Central Limit Theorem states that the mean of the sampling distribution of
the sample mean is
A. larger than the population mean.
B. exactly equal to the population mean.
C. equal to the population mean divided by the square root of the sample size.
D. close to the population means if the sample size is large.
4. Which of the following descriptions about Central Limit Theorem is NOT essential?
A. The larger the sample, the better approximation will be.
B. The smaller the sample, the bigger the approximation will be.
C. When the original variable is normally distributed, the distribution of the
sample means will be normally distributed for any sample size n.
D. When the distribution of the original variable might not be normal, a sample
size of 30 or more is needed to use a normal distribution to approximate the
distribution of the sample means.
5. Suppose the average age of family members is 34 with a standard deviation of 4.
If 100 members of the community decided to have a summer outing bonding and
relaxation, find the probability that the average of these members is less than 35?
A. 91.32%
C. 95%
B. 94.45%
D. 99.38%​