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This module provides a number of homework/review problems related to Continuous Random Variables.

[link][link] refer to the following study: A recent study of mothers of junior high school children in Santa Clara County reported that 76% of the mothers are employed in paid positions. Of those mothers who are employed, 64% work full-time (over 35 hours per week), and 36% work part-time. However, out of all of the mothers in the population, 49% work full-time. The population under study is made up of mothers of junior high school children in Santa Clara County.

Let E = size 12{E={}} {} employed, Let F = size 12{F={}} {} full-time employment

  • Find the percent of all mothers in the population that NOT employed.
  • Find the percent of mothers in the population that are employed part-time.
  • 24%
  • 27%
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The type of employment is considered to be what type of data?

Qualitative

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Find the probability that a randomly selected mother works part-time given that she is employed.

0.36

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Find the probability that a randomly selected person from the population will be employed OR work full-time.

0.7636

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Based upon the above information, are being employed AND working part-time:

  • mutually exclusive events? Why or why not?
  • independent events? Why or why not?
  • No,
  • No,
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[link] - [link] refer to the following: We randomly pick 10 mothers from the above population. We are interested in the number of the mothers that are employed. Let X = size 12{X={}} {} number of mothers that are employed.

State the distribution for X size 12{X} {} .

B ( 10 , 0 . 76 ) size 12{B \( "10",0 "." "76" \) } {}

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Find the probability that at least 6 are employed.

0.9330

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We expect the Statistics Discussion Board to have, on average, 14 questions posted to it per week. We are interested in the number of questions posted to it per day.

  • Define X size 12{X} {} .
  • What are the values that the random variable may take on?
  • State the distribution for X size 12{X} {} .
  • Find the probability that from 10 to 14 (inclusive) questions are posted to the Listserv on a randomly picked day.
  • X = size 12{X={}} {} the number of questions posted to the Statistics Listserv per day
  • x = 0,1,2, . . . size 12{x=0,1,2, "." "." "." } {}
  • X ~ P ( 2 ) size 12{X "~" P \( 2 \) } {}
  • 0
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A person invests $1000 in stock of a company that hopes to go public in 1 year.

  • The probability that the person will lose all his money after 1 year (i.e. his stock will be worthless) is 35%.
  • The probability that the person’s stock will still have a value of $1000 after 1 year (i.e. no profit and no loss) is 60%.
  • The probability that the person’s stock will increase in value by $10,000 after 1 year (i.e. will be worth $11,000) is 5%.

Find the expected PROFIT after 1 year.

$150

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Rachel’s piano cost $3000. The average cost for a piano is $4000 with a standard deviation of $2500. Becca’s guitar cost $550. The average cost for a guitar is $500 with a standard deviation of $200.Matt’s drums cost $600. The average cost for drums is $700 with a standard deviation of $100. Whose cost was lowest when compared to his or her own instrument? Justify your answer.

Matt

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Horizontal boxplot with first whisker extending from 1 to 2, box from 2 to 5,  line at 4, and second whisker extending from 5 to 7.

For each statement below, explain why each is either true or false.

  • 25% of the data are at most 5.
  • There is the same amount of data from 4 – 5 as there is from 5 – 7.
  • There are no data values of 3.
  • 50% of the data are 4.
  • False
  • True
  • False
  • False
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[link][link] refer to the following: 64 faculty members were asked the number of cars they owned (including spouse and children’s cars). The results are given in the following graph: Histogram consisting of 5 bars with number of cars, from 0-7 in increments of 1, on the x-axis, and frequency, in increments of 0.1 from 0.15-0.45, on the y-axis. No bars exist for 4, 5, or 7. Bar 0 has a frequency of 0.075, 1 has 0.15, 2 has 0.45, 3 has 0.25, and 6 has 0.075.

Find the approximate number of responses that were “3.”

16

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Find the first, second and third quartiles. Use them to construct a box plot of the data.

2,2,3 size 12{2,2,3} {}

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[link][link] refer to the following study done of the Girls soccer team “Snow Leopards”:

Hair Style Hair Color
blond brown black
ponytail 3 2 5
plain 2 2 1
Suppose that one girl from the Snow Leopards is randomly selected.

Find the probability that the girl has black hair GIVEN that she wears a ponytail.

5 10 = 0 . 5 size 12{ { {5} over {"10"} } =0 "." 5} {}

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Find the probability that the girl wears her hair plain OR has brown hair.

7 15 size 12{ { {7} over {"15"} } } {}

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Find the probability that the girl has blond hair AND that she wears her hair plain.

2 15 size 12{ { {2} over {"15"} } } {}

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Questions & Answers

What are the factors that affect demand for a commodity
Florence Reply
differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
how will I do?
Venny Reply
how is the graph works?I don't fully understand
Rezat Reply
information
Eliyee
devaluation
Eliyee
t
WARKISA
hi guys good evening to all
Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
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
What is ceteris paribus?
Shukri Reply
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
yes,thank you
Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
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
ok
Shukri
how do you save a country economic situation when it's falling apart
Lilia Reply
what is the difference between economic growth and development
Fiker Reply
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 ?
Abdisa Reply
any question about economics?
Awais Reply
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 .
Feyisa Reply
Answer
Feyisa
c
Jabir
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
Gsbwnw Reply
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. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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