# 7.1 Homework: clt (modified r. bloom)

 Page 1 / 3
Homework problems for Central Limit Theorem for the textbook collection Collaborative Statistics by Susan Dean and Dr. Barbara Illowsky; their original module has been modified to include more questions about CLT for means and eliminate questions about CLT for sums.

$X$ ~ $N\left(\text{60},9\right)$ . Suppose that you form random samples of 25 from this distribution. Let $\overline{X}$ be the random variable of averages. For c - f , sketch the graph, shade the region, label and scale the horizontal axis for $\overline{X}$ , and find the probability.

• Sketch the distributions of $X$ and $\overline{X}$ on the same graph.
• $\overline{X}$ ~
• $P\left(\overline{X}<\text{60}\right)=$
• Find the 30th percentile.
• $P\left(\text{56}<\overline{X}<\text{62}\right)=$
• $P\left(\text{18}<\overline{X}<\text{58}\right)=$
• Find the minimum value for the upper quartile.
• $\text{Xbar}\text{~}N\left(\text{60},\frac{9}{\sqrt{\text{25}}}\right)$
• 0.5000
• 59.06
• 0.8536
• 0.1333
• 61.214

Determine which of the following are true and which are false. Then, in complete sentences, justify your answers.

• When the sample size is large, the mean of $\overline{X}$ is approximately equal to the mean of $X$ .
• When the sample size is large, $\overline{X}$ is approximately normally distributed.
• When the sample size is large, the standard deviation of $\overline{X}$ is approximately the same as the standard deviation of $X$ .

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen.

Let $\overline{X}=$ average percent of fat calories.

• $\overline{X}\text{~}$ ______ ( ______ , ______ )
• For the group of 16, find the probability that the average percent of fat calories consumed is more than 5. Graph the situation and shade in the area to be determined.
• Find the first quartile for the average percent of fat calories.
• $N\left(\text{36},\frac{\text{10}}{\sqrt{\text{16}}}\right)$
• 1
• 34.31

Previously, De Anza statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students. • In words, $X=$ • $X\text{~}$ • In words, $\overline{X}=$ • $\overline{X}\text{~}$ ______ ( ______ , ______ ) • Find the probability that an individual had between$0.80 and $1.00. Graph the situation and shade in the area to be determined. • Find the probability that the average of the 25 students was between$0.80 and $1.00. Graph the situation and shade in the area to be determined. • Explain the why there is a difference in (e) and (f). Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. • If $\overline{X}=$ average distance in feet for 49 fly balls, then $\overline{X}\text{~}$ _______ ( _______ , _______ ) • What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for $\overline{X}$ . Shade the region corresponding to the probability. Find the probability. • Find the 80th percentile of the distribution of the average of 49 fly balls. • $N\left(\text{250},\frac{\text{50}}{\sqrt{\text{49}}}\right)$ • 0.0808 • 256.01 feet Question removed from textbook. Note: Problem has been changed from original version of textbook. Suppose that the duration of a particular type of criminal trial is known to have a mean of 21 days and a standard deviation of 7 days. We randomly sample 25 trials. • Find the probability that the average length of the 25 trials is at least 24 days. • Find the 10th percentile for the average length for samples of 25 trials of this type. • Answer: 0.0161 • Answer: 19.2 days #### Questions & Answers what is the meaning of function in economics Effah Reply Pls, I need more explanation on price Elasticity of Supply Isaac Reply Is the degree to the degree of responsiveness of a change in quantity supplied of goods to a change in price Afran Discuss the short-term and long-term balance positions of the firm in the monopoly market? Rabindranath Reply hey Soumya hi Mitiku how are you? Mitiku can you tell how can i economics honurs(BSC) in reputed college? Soumya through hard study and performing well than expected from you Mitiku what should i prepare for it? Soumya prepare first, in psychologically as well as potentially to sacrifice what's expected from you, when I say this I mean that you have to be ready, for every thing and to accept failure as a good and you need to change them to potential for achievement of ur goals Mitiku parna kya hai behencho? Soumya Hallo Rabindranath Hello, dear what's up? Mitiku cool Momoh good morning Isaac pls, is anyone here from Ghana? Isaac Hw s every one please Afran Ys please I'm in Ghana Afran what is firms Anteyi Reply A firm is a business entity which engages in the production of goods and aimed at making profit. Avuwada What is autarky in Economics. Avuwada what is choice Tia Reply So how is the perfect competition different from others Rev Reply what is choice Tia please what type of commodity is 1.Beaf 2.Suagr 3.Bread Alfred Reply 1 Naziru what is the difference between short run and long run? Ukpen Reply It just depends on how far you would like to run!!!🤣🤣🤣 Anna meaning? You guys need not to be playing here; if you don't know a question, leave it for he that knows. Ukpen pls is question from which subject or which course Ada Is this not economics? Ukpen This place is meant to be for serious educational matters n not playing ground so pls let's make it a serious place. Docky Is there an economics expert here? Docky Okay and I was being serous Anna The short run is a period of time in which the quantity of at least one inputs is fixed... Anna that is the answer that I found online and in my text book Anna Elacisity salihu Meaning of economics Suraj Reply It will creates rooms for an effective demands. Chinedum Reply different between production and supply babsnof Hii Suraj hlo eshita What is the economic? Suraj Economics is a science which study human behavior as a relationship between ends and scarce means which has an alternative use. Mr what is supply babsnof what is different between demand and supply Debless Reply Demand refers to the quantity of products that consumers are willing to purchase at various prices per time while Supply has to do with the quantity of products suppliers are willing to supply at various prices per time. find the difference in between Saye Please what are the effects of rationing Effect of black market Effects of hoarding Atty Reply monoply is amarket structure charecrized by asingle seller and produce a unique product in the market Cali Reply yes Niraj I want to know wen does the demand curve shift to the right Nana demand curve shifts to the right when there's an increase in price of a substitute or increase in income kin ask me anything in economics, I promise to try and do justice to the question, you can send me an email or message, I will answer kin what are the factor that change the curve right Nana explain the law of supply in simple ..... freshwater the Law of supply: states that all factor being equal, when the price of a particular goods increase the supply will also increase, as it decreases the supply will also decrease kin @Nana the factor that changes or shift the d demand curve to the right is 1) the increase in price of a substitute good or commodity 2) increase in income kin you can send your questions I am Comr. Kin chukwuebuka kin different between bill of exchange n treasure bill Nana yes Ada so would you tell me what means an apportunity cost plz? Cali what is true cost Akiti your question isn't correct naadi Anthonia define an apportunity cost? Cali orukpe ,is my question whats wrong or u dont know anything? Cali In a simple term, it is an Alternative foregone. Sule opportunity cost is the next best value of a scale of preference Akiti Both of you are not correct. Nelly opportunity cost: is a forgone alternative kin Monopoly is where is one producer produces a given product with no close substitute James what is income effect? Qwecou Reply if you borrow$5000 to buy a car at 12 percent compounded monthly to be repaid over the next 4 year what is monthly payment
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
Got questions? Join the online conversation and get instant answers!   By    By Rhodes By Dravida Mahadeo-J... By By