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References

“Naegele’s rule.” Wikipedia. Available online at http://en.wikipedia.org/wiki/Naegele's_rule (accessed May 14, 2013).

“403: NUMMI.” Chicago Public Media&Ira Glass, 2013. Available online at http://www.thisamericanlife.org/radio-archives/episode/403/nummi (accessed May 14, 2013).

“Scratch-Off Lottery Ticket Playing Tips.” WinAtTheLottery.com, 2013. Available online at http://www.winatthelottery.com/public/department40.cfm (accessed May 14, 2013).

“Smart Phone Users, By The Numbers.” Visual.ly, 2013. Available online at http://visual.ly/smart-phone-users-numbers (accessed May 14, 2013).

“Facebook Statistics.” Statistics Brain. Available online at http://www.statisticbrain.com/facebook-statistics/(accessed May 14, 2013).

Chapter review

The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one. The parameters of the normal are the mean µ and the standard deviation σ . A special normal distribution, called the standard normal distribution is the distribution of z -scores. Its mean is zero, and its standard deviation is one.

Formula review

Normal Distribution: X ~ N ( µ , σ ) where µ is the mean and σ is the standard deviation.

Standard Normal Distribution: Z ~ N (0, 1).

Calculator function for probability: normalcdf (lower x value of the area, upper x value of the area, mean, standard deviation)

Calculator function for the k th percentile: k = invNorm (area to the left of k , mean, standard deviation)

How would you represent the area to the left of one in a probability statement?

P ( x <1)

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What is the area to the right of one?

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Is P ( x <1) equal to P ( x ≤ 1)? Why?

Yes, because they are the same in a continuous distribution: P ( x = 1) = 0

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How would you represent the area to the left of three in a probability statement?

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What is the area to the right of three?

1 – P ( x <3) or P ( x >3)

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If the area to the left of x in a normal distribution is 0.123, what is the area to the right of x ?

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If the area to the right of x in a normal distribution is 0.543, what is the area to the left of x ?

1 – 0.543 = 0.457

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Use the following information to answer the next four exercises:

X ~ N (54, 8)

Find the probability that x >56.

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Find the probability that x <30.

0.0013

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Find the 80 th percentile.

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Find the 60 th percentile.

56.03

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X ~ N (6, 2)

Find the probability that x is between three and nine.

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X ~ N (–3, 4)

Find the probability that x is between one and four.

0.1186

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X ~ N (4, 5)

Find the maximum of x in the bottom quartile.

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Use the following information to answer the next three exercise: The life of Sunshine CD players is normally distributed with a mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts. Find the probability that a CD player will break down during the guarantee period.

  1. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.
    Empty normal distribution curve.
  2. P (0< x <____________) = ___________ (Use zero for the minimum value of x .)
  1. Check student’s solution.
  2. 3, 0.1979
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Find the probability that a CD player will last between 2.8 and six years.

  1. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.
    Empty normal distribution curve.
  2. P (__________< x <__________) = __________
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Find the 70 th percentile of the distribution for the time a CD player lasts.

  1. Sketch the situation. Label and scale the axes. Shade the region corresponding to the lower 70%.
    Empty normal distribution curve.
  2. P ( x < k ) = __________ Therefore, k = _________
  1. Check student’s solution.
  2. 0.70, 4.78 years
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Questions & Answers

20 25 find the area under the normal curve
Akram Reply
find the area normal curve
Akram
Let x1, x2, ...,xn be a random sample of size n from N(0,σ  ), show that there exists an UMP test with significance level α for testing H0 :  2 =  2 against H1 :  2 <  2 . If n=15,  = 0.05, and  2= 3, determine the BCR
Bhavana Reply
3xy^2√[x^3y^2/(12(x^3y)^2)]
Esther Reply
what is probability
Esther
what is probability
Esther
what is probability
Esther
Probability is a branch of mathematics that deals with the occurrence of a random event. For example, when a coin is tossed in the air, the possible outcomes are Head and Tail.
Dewan
mean 0 and standard deviation 1 .using area table find P(X>3)
Naeem Reply
what is terms data?
Mohsin Reply
define the types of data?
Mohsin
define the number of classes?
Mohsin
define the class limt?
Mohsin
define the class frequency and class interval ?
Mohsin
define class boundaries
George
Your home address nominal Interval ratio ordinal
MD
home address is nominal
Awel
what is axioms of probability
Khaleed Reply
characteristics of statistic
Safi Reply
a measure of cntral tendency is a quantitative value that tends to locate in some sense the middle of a set of data
khan Reply
in a large metropolitan area
Vernon Reply
a lecturer claims that his students score an average of 55 marks in their statistics test. the object supervisor wants to know wether the lecturer's claims is acceptable or not.what is the posible tail of the test?
Karen
2
J-zil
the best sampling method for A school has a total of 100 teachers. Each teacher in the school is given a number and then a random sample of 35 teachers is obtained.
Nurhaznissah Reply
what the best sampling method for A school has a total of 100 teachers. Each teacher in the school is given a number and then a random sample of 35 teachers is obtained.
Nurhaznissah
option please
Dewan
systematic
Dewan
any one send me the notes of these chpt if possible introduction to statistics measure of centeral tendency or average measure of dispensation moments and skewness presentation of data
Aqsa Reply
Kindly send me these notes.
Naheed
normal distribution
Akram
statistics
Akram
what is a regression, and what is it primarily used for
Denisha Reply
assume the sample populations do not have equal standard deviations and use the 0.05 significance level
Nokuthula Reply
what is the solution to this question?
Manbyen Reply
hi
Dewan
hello
Learn
hi please tell
Dewan
The controls that are usually used are
Rushikesh Reply
what is math
Rushikesh
the controls that are usually used in quality controls and also controls a process is key tool used in run chat, control chat and design of experiment etc.,
Sravanthi

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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