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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 ( 60 , 9 ) size 12{X "~" N \( "60",9 \) } {} . Suppose that you form random samples of 25 from this distribution. Let X ¯ size 12{ {overline {X}} } {} be the random variable of averages. For c - f , sketch the graph, shade the region, label and scale the horizontal axis for X ¯ size 12{ {overline {X}} } {} , and find the probability.

  • Sketch the distributions of X size 12{X} {} and X ¯ size 12{ {overline {X}} } {} on the same graph.
  • X ¯ size 12{ {overline {X}} "~" } {} ~
  • P ( X ¯ < 60 ) = size 12{P \( {overline {X}}<"60" \) ={}} {}
  • Find the 30th percentile.
  • P ( 56 < X ¯ < 62 ) = size 12{P \( "56"<{overline {X}}<"62" \) ={}} {}
  • P ( 18 < X ¯ < 58 ) = size 12{P \( "18"<{overline {X}}<"58" \) ={}} {}
  • Find the minimum value for the upper quartile.
  • Xbar ~ N ( 60 , 9 25 ) size 12{ ital "Xbar" "~" N \( "60", { {9} over { sqrt {"25"} } } \) } {}
  • 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 X ¯ size 12{ {overline {X}} } {} is approximately equal to the mean of X size 12{X} {} .
  • When the sample size is large, X ¯ size 12{ {overline {X}} } {} is approximately normally distributed.
  • When the sample size is large, the standard deviation of X ¯ size 12{ {overline {X}} } {} is approximately the same as the standard deviation of X size 12{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 X ¯ = size 12{ {overline {X}} ={}} {} average percent of fat calories.

  • X ¯ ~ size 12{ {overline {X}} "~" } {} ______ ( ______ , ______ )
  • 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 ( 36 , 10 16 ) size 12{ ital "Xbar" "~" N \( "36", { {"10"} over { sqrt {"16"} } } \) } {}
  • 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 = size 12{X={}} {}
  • X ~ size 12{X "~" } {}
  • In words, X ¯ = size 12{ {overline {X}} ={}} {}
  • X ¯ ~ size 12{ {overline {X}} "~" } {} ______ ( ______ , ______ )
  • 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 X ¯ = size 12{ {overline {X}} ={}} {} average distance in feet for 49 fly balls, then X ¯ ~ size 12{ {overline {X}} "~" } {} _______ ( _______ , _______ )
  • What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X ¯ size 12{ {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 ( 250 , 50 49 ) size 12{ ital "Xbar" "~" N \( "250", { {"50"} over { sqrt {"49"} } } \) } {}
  • 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
Discuss the short-term and long-term balance positions of the firm in the monopoly market?
Rabindranath Reply
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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
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Hello, dear what's up?
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what is firms
Anteyi Reply
A firm is a business entity which engages in the production of goods and aimed at making profit.
What is autarky in Economics.
what is choice
Tia Reply
So how is the perfect competition different from others
Rev Reply
what is choice
please what type of commodity is 1.Beaf 2.Suagr 3.Bread
Alfred Reply
what is the difference between short run and long run?
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It just depends on how far you would like to run!!!🤣🤣🤣
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Is there an economics expert here?
Okay and I was being serous
The short run is a period of time in which the quantity of at least one inputs is fixed...
that is the answer that I found online and in my text book
Meaning of economics
Suraj Reply
It will creates rooms for an effective demands.
Chinedum Reply
different between production and supply
What is the economic?
Economics is a science which study human behavior as a relationship between ends and scarce means which has an alternative use.
what is supply
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
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
I want to know wen does the demand curve shift to the right
demand curve shifts to the right when there's an increase in price of a substitute or increase in income
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what are the factor that change the curve right
explain the law of supply in simple .....
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
@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
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different between bill of exchange n treasure bill
so would you tell me what means an apportunity cost plz?
what is true cost
your question isn't correct naadi
define an apportunity cost?
orukpe ,is my question whats wrong or u dont know anything?
In a simple term, it is an Alternative foregone.
opportunity cost is the next best value of a scale of preference
Both of you are not correct.
opportunity cost: is a forgone alternative
Monopoly is where is one producer produces a given product with no close substitute
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
Nitish Reply
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
Mapo Reply
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
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Source:  OpenStax, Collaborative statistics homework book: custom version modified by r. bloom. OpenStax CNX. Dec 23, 2009 Download for free at http://legacy.cnx.org/content/col10619/1.2
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