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5.6 Practice 2: exponential distribution

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In this module the student will explore the properties of data with an exponential distribution.

Student learning outcomes

  • The student will analyze data following the exponential distribution.

Given

Carbon-14 is a radioactive element with a half-life of about 5730 years. Carbon-14 is said to decay exponentially. The decay rate is 0.000121 . We start with 1 gram of carbon-14. We are interested in the time (years) it takes to decay carbon-14.

Describe the data

What is being measured here?

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Are the data discrete or continuous?

Continuous

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In words, define the Random Variable X size 12{X} {} .

X size 12{X} {} = Time (years) to decay carbon-14

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What is the decay rate ( m size 12{m} {} )?

m size 12{m} {} = 0.000121

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The distribution for X size 12{X} {} is:

X size 12{X} {} ~ Exp(0.000121)

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Probability

Find the amount (percent of 1 gram) of carbon-14 lasting less than 5730 years. This means, find P ( x < 5730 ) size 12{P \( X<"5730" \) } {} .

  • Sketch the graph. Shade the area of interest.
    Blank graph with vertical and horizontal axes.
  • Find the probability. P ( x < 5730 ) size 12{P \( X<"5730" \) } {} =
  • P ( x < 5730 ) size 12{P \( X<"5730" \) } {} = 0.5001
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Find the percentage of carbon-14 lasting longer than 10,000 years.

  • Sketch the graph. Shade the area of interest.
    Blank graph with horizontal and vertical axes.
  • Find the probability. P ( x > 10000 ) size 12{P \( X<"5730" \) } {} =
  • P ( x > 10000 ) size 12{P \( X<"5730" \) } {} = 0.2982
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Thirty percent (30%) of carbon-14 will decay within how many years?

  • Sketch the graph. Shade the area of interest.
    Blank graph with vertical and horizontal axes.
  • Find the value k size 12{k} {} such that P ( x < k ) = 0 . 30 size 12{P \( X<k \) =0 "." "30"} {} .
  • k size 12{k} {} = 2947.73
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Questions & Answers

Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
Widad Reply
can you send the book attached ?
Ariel
?
Ariel
What is economics
Widad Reply
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn Reply
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn
what is ecnomics
Jan Reply
this is the study of how the society manages it's scarce resources
Belonwu
what is macroeconomic
John Reply
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
etc
husaini
difference between firm and industry
husaini Reply
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from Qd  120 3P to Qd  90  3P and the supply function has shifted from QS  20  2P to QS 10  2P . a) Find the effect of this change on price and quantity. b) Which of the changes in demand and supply is higher?
Toofiq Reply
explain standard reason why economic is a science
innocent Reply
factors influencing supply
Petrus Reply
what is economic.
Milan Reply
scares means__________________ends resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Zarshad Reply
Why qualify 28 supplies
Milan
what are explicit costs
Nomsa Reply
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
David Reply
economic overview notes
Amahle Reply
identify a demand and a supply curve
Salome Reply
i don't know
Parul
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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