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- Collaborative statistics teacher
- Collaborative statistics teacher
- Ch. 7: central limit theroem
This module is the complementary teacher's guide for the Central Limit Theorem chapter of the Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
The Central Limit Theorem (CLT) is considered to be one of the most powerful theorems in all of statistics and probability. It states that if you draw samples of size
and average (or sum) them, you will get a distribution of averages (or sums) that follow a normal distribution.
Suppose
and
are the original mean and standard deviation of the population from which each sample of size
is drawn. Let
= the random variable for the average of
samples. Let
= the random variable for the number of
samples
The dice experiment
At the beginning of the chapter, there is a dice experiment. Together with the students, do the experiment. The example consists of rolling 10 times each, 1 die, 2 dice, 5 dice, and 10 dice and averaging the faces. Draw graphs (histograms are OK). This experiment, most of the time, shows that, as the number of dice increase, the graph looks more and more bell-shaped. Because the samples taken are usually small, you will not necessarily get a perfect bell-shaped curve. However, the students should get the idea.
Calculate averages
It can be shown that the average amount of money one person spends on one trip to a particular supermarket is $51. The averages follow an exponential distribution.
Find the probability that the average of 40 samples is more than $60.
Let
= the average amount of money that 40 people spend. Have the students draw the appropriate picture, labeling the x-axis with
. The mean
and the standard deviation
. If you are using the TI-83/84 series, use the function
normalcdf(60, 10^99, 51, 51/40) .
The 75th percentile for the average amount spent by 40 people at the supermarket is $56.44. This means that 75% of the people spend no more than $56.44 and 25% spend no less than that amount.
This can be calculated by using the TI-83/84 function
InvNorm(.75, 51, 51/ 40) .
Calculate sums
You can also do examples for sums. We, the authors, do not do sums because of time (we are on a quarter system). Help the students to find the probability that the total (sum) amount of money spent by 10 people at the supermarket is less than $500. Also, help them do a percentile problem.
If you want to teach the z-score formulas for averages and sums, they are:
Assign practice
Assign the
Practice in class to be done in groups.
Assign homework
Assign
Homework . Suggested homework: (averages) 1a - f, 3, 5, 9, 10, 11a - d, f, k, 13a-c,g-j, 16, 17, 19 - 23
Questions & Answers
What are the factors that affect demand for a commodity
differentiate between demand and supply
giving examples
differentiated between demand and supply using examples
Lambiv
how is the graph works?I don't fully understand
hi guys good evening to all
Lambiv
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
Can I ask you other question?
Shukri
What is different between quantity demand and demand?
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
how do you save a country economic situation when it's falling apart
what is the difference between economic growth and development
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
any question about economics?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
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Source:
OpenStax, Collaborative statistics teacher's guide. OpenStax CNX. Oct 01, 2008 Download for free at http://cnx.org/content/col10547/1.5
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