The Central Limit Theorem
A) Create a distribution with 50 observations of 1, 20
observations of 2, 60 observations of 3, 30 observations of 4, 30
observations of 5, and 90 observations of 6 (Hint: use the rep()
command). Plot a histogram of this distribution (Hint: adjust the
breaks if necessary).
B) Take 1,000 samples of size 10 from the distribution (with
replacement). Calculate the mean for each sample and plot the
distribution of these means.
C) Take 1,000 samples...
This week we’ve introduced the central limit theorem. According to
the central limit theorem, for all samples of the same size n with
n>30, the sampling distribution of x can be approximated by a
normal distribution.
In your initial post
use your own words to explain what this theorem means. Then provide
a quick example to explain how this theorem might apply in real
life. At last, please share with us your thoughts about why this
theorem is important.
3. Probability+ Central Limit Theorem questions:
a. The return on investment is normally distributed with a mean
of 10% and a standard deviation of 5%. What is the probability of
losing money?
b. An average male drinks 2 liter of water when active outdoor
(with a standard deviation of 0.7). An organization is planning for
a full day outdoor for 50 men and will bring 110 liter of water.
What is the probability that the organization will run out of...
3.27. Problem. (Section 11.5) The following are applications of
Theorem 11.6 or the Central Limit Theorem.
(a) Determine the distribution of (1/5)X1 + (2
/5)X2 + (2/5)X3 if X1,
X2 and X3 are independent normal
distributions with µ = 2 and
σ = 3.
(b) The weight (kg) of a StarBrite watermelon harvested under
certain environmental conditions is normally distributed with a
mean of 8.0 with standard deviation of 1.9. Suppose 24 StarBrite
watermelons grown in these conditions are harvested;...
Using the Central Limit Theorem, how can we be confident that
this public opinion polling tells us information about a larger
population by taking a sample?