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This module provides a number of homework exercises related to Continuous Random Variables.

For each probability and percentile problem, DRAW THE PICTURE!

Consider the following experiment. You are one of 100 people enlisted to take part in a study to determine the percent of nurses in America with an R.N. (registered nurse) degree. You ask nurses if they have an R.N. degree. The nurses answer “yes” or “no.” You then calculate the percentage of nurses with an R.N. degree. You give that percentage to your supervisor.

  • What part of the experiment will yield discrete data?
  • What part of the experiment will yield continuous data?
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When age is rounded to the nearest year, do the data stay continuous, or do they become discrete? Why?

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Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform Distribution from 1 – 53 (spread of 52 weeks).

  • X size 12{X} {} ~
  • Graph the probability distribution.
  • f ( x ) size 12{f \( x \) } {} =
  • μ size 12{μ} {} =
  • σ size 12{σ} {} =
  • Find the probability that a person is born at the exact moment week 19 starts. That is, find P ( x = 19 ) size 12{P \( X="19" \) } {} =
  • P ( 2 < x < 31 ) = size 12{P \( 2<X<"31" \) ={}} {}
  • Find the probability that a person is born after week 40.
  • {} P ( 12 < x x < 28 ) size 12{P \( "12"<X \lline X<"28" \) } {} =
  • Find the 70th percentile.
  • Find the minimum for the upper quarter.
  • X ~ U ( 1, 53 ) size 12{X " ~ " U \( 1,"53" \) } {}
  • f ( x ) = 1 52 size 12{f \( x \) = { {1} over { \( b - a \) } } = { {1} over { \( "53" - 1 \) } } = { {1} over {"52"} } } {} where 1 x 53 size 12{1<= x<= "53"} {}
  • 27
  • 15.01
  • 0
  • 29 52
  • 13 52
  • 16 27
  • 37.4
  • 40
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A random number generator picks a number from 1 to 9 in a uniform manner.

  • X ~ size 12{X "~" } {}
  • Graph the probability distribution.
  • f ( x ) = size 12{f \( x \) ={}} {}
  • μ = size 12{μ={}} {}
  • σ = size 12{σ={}} {}
  • P ( 3 . 5 < x < 7 . 25 ) = size 12{P \( 3 "." 5<X<7 "." "25" \) ={}} {}
  • P ( x > 5 . 67 ) = size 12{P \( X>5 "." "67" \) ={}} {}
  • P ( x > 5 x > 3 ) = size 12{P \( X>5 \lline X>3 \) ={}} {}
  • Find the 90th percentile.
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The time (in minutes) until the next bus departs a major bus depot follows a distribution with f ( x ) = 1 20 where x goes from 25 to 45 minutes.

  • Define the random variable. X = size 12{X={}} {}
  • X ~ size 12{X "~" } {}
  • Graph the probability distribution.
  • The distribution is ______________ (name of distribution). It is _____________ (discrete or continuous).
  • μ = size 12{μ={}} {}
  • σ = size 12{σ={}} {}
  • Find the probability that the time is at most 30 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
  • Find the probability that the time is between 30 and 40 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
  • P ( 25 < x < 55 ) = size 12{P \( "25"<X<"55" \) ={}} {} _________. State this in a probability statement (similar to g and h ), draw the picture, and find the probability.
  • Find the 90th percentile. This means that 90% of the time, the time is less than _____ minutes.
  • Find the 75th percentile. In a complete sentence, state what this means. (See j .)
  • Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 30 minutes.
  • X ~ U ( 25 , 45 ) size 12{X "~" U \( "25","45" \) } {}
  • uniform; continuous
  • 35 minutes
  • 5.8 minutes
  • 0.25
  • 0.5
  • 1
  • 43 minutes
  • 40 minutes
  • 0.3333
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According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between 6 and 15 pounds a month until they approach trim body weight. Let’s suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month. (Source: The McDougall Program for Maximum Weight Loss by John A. McDougall, M.D.)

  • Define the random variable. X = size 12{X={}} {}
  • X ~ size 12{X "~" } {}
  • Graph the probability distribution.
  • f ( x ) = size 12{f \( x \) ={}} {}
  • μ = size 12{μ={}} {}
  • σ = size 12{σ={}} {}
  • Find the probability that the individual lost more than 10 pounds in a month.
  • Suppose it is known that the individual lost more than 10 pounds in a month. Find the probability that he lost less than 12 pounds in the month.
  • P ( 7 < x < 13 x > 9 ) = size 12{P \( 7<X<"13" \lline X>9 \) ={}} {} __________. State this in a probability question (similar to g and h), draw the picture, and find the probability.
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Questions & Answers

what is mutation
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what is a cell
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classification of plants, gymnosperm features.
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What is Atoms
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urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
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State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
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how is urine formed in human
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malaria is caused by an insect called mosquito.
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Malaria is cause by female anopheles mosquito
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Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
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a canal is more needed in a root but a cavity is a bad effect
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what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
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how are lungs work
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in the mouth
EZEKIEL
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stimulates the follicle to release the mature ovum into the oviduct
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endocrine secrete hormone and regulate body process
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while pituitary gland is an example of endocrine system and it's found in the Brain
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Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
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Biology is the study of how living organisms live and survive in a specific environment
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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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