<< Chapter < Page Chapter >> Page >

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)

Got questions? Get instant answers now!

What is the area to the right of one?

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

What is the area to the right of three?

1 – P ( x <3) or P ( x >3)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Use the following information to answer the next four exercises:

X ~ N (54, 8)

Find the probability that x >56.

Got questions? Get instant answers now!

Find the probability that x <30.

0.0013

Got questions? Get instant answers now!

Find the 80 th percentile.

Got questions? Get instant answers now!

Find the 60 th percentile.

56.03

Got questions? Get instant answers now!

X ~ N (6, 2)

Find the probability that x is between three and nine.

Got questions? Get instant answers now!

X ~ N (–3, 4)

Find the probability that x is between one and four.

0.1186

Got questions? Get instant answers now!

X ~ N (4, 5)

Find the maximum of x in the bottom quartile.

Got questions? Get instant answers now!

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
Got questions? Get instant answers now!

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 <__________) = __________
Got questions? Get instant answers now!

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
Got questions? Get instant answers now!

Questions & Answers

what is confidence interval estimate and its formula in getting it
Jhezarie Reply
discuss the roles of vital and health statistic in the planning of health service of the community
BITRUS Reply
given that the probability of
BITRUS
can man city win Liverpool ?
Emmanuel Reply
There are two coins on a table. When both are flipped, one coin land on heads eith probability 0.5 while the other lands on head with probability 0.6. A coin is randomly selected from the table and flipped. (a) what is probability it lands on heads? (b) given that it lands on tail, what is the Condi
Nusrat Reply
0.5*0.5+0.5*0.6
Ravasz
what is gradient descent?
Saurav Reply
It should be a Machine learning terms。
Mok
it is a term used in linear regression
Saurav
what are the differences between standard deviation and variancs?
Enhance
what is statistics
Emmanuel Reply
statistics is the collection and interpretation of data
Enhance
the science of summarization and description of numerical facts
Enhance
Is the estimation of probability
Zaini
mr. zaini..can u tell me more clearly how to calculated pair t test
Haai
do you have MG Akarwal Statistics' book Zaini?
Enhance
Haai how r u?
Enhance
maybe .... mathematics is the science of simplification and statistics is the interpretation of such values and its implications.
Miguel
can we discuss about pair test
Haai
what is outlier?
Usama Reply
outlier is an observation point that is distant from other observations.
Gidigah
what is its effect on mode?
Usama
Outlier  have little effect on the mode of a given set of data.
Gidigah
How can you identify a possible outlier(s) in a data set.
Daniel
The best visualisation method to identify the outlier is box and wisker method or boxplot diagram. The points which are located outside the max edge of wisker(both side) are considered as outlier.
Akash
@Daniel Adunkwah - Usually you can identify an outlier visually. They lie outside the observed pattern of the other data points, thus they're called outliers.
Ron
what is completeness?
Muhammad
I am new to this. I am trying to learn.
Dom
I am also new Dom, welcome!
Nthabi
thanks
Dom
please my friend i want same general points about statistics. say same thing
alex
outliers do not have effect on mode
Meselu
also new
yousaf
I don't get the example
Hadekunle Reply
ways of collecting data at least 10 and explain
Ridwan Reply
Example of discrete variable
Bada Reply
sales made monthly.
Gbenga
I am new here, can I get someone to guide up?
alayo
dies outcome is 1, 2, 3, 4, 5, 6 nothing come outside of it. it is an example of discrete variable
jainesh
continue variable is any value value between 0 to 1 it could be 4digit values eg 0.1, 0.21, 0.13, 0.623, 0.32
jainesh
How to answer quantitative data
Alhassan Reply
hi
Kachalla
what's up here ... am new here
Kachalla
sorry question a bit unclear...do you mean how do you analyze quantitative data? If yes, it depends on the specific question(s) you set in the beginning as well as on the data you collected. So the method of data analysis will be dependent on the data collecter and questions asked.
Bheka
how to solve for degree of freedom
saliou
Quantitative data is the data in numeric form. For eg: Income of persons asked is 10,000. This data is quantitative data on the other hand data collected for either make or female is qualitative data.
Rohan
*male
Rohan
Degree of freedom is the unconditionality. For example if you have total number of observations n, and you have to calculate variance, obviously you will need mean for that. Here mean is a condition, without which you cannot calculate variance. Therefore degree of freedom for variance will be n-1.
Rohan
data that is best presented in categories like haircolor, food taste (good, bad, fair, terrible) constitutes qualitative data
Bheka
vegetation types (grasslands, forests etc) qualitative data
Bheka
I don't understand how you solved it can you teach me
Caleb Reply
solve what?
Ambo
mean
Vanarith
What is the end points of a confidence interval called?
ZIMKHITHA Reply
lower and upper endpoints
Bheka
Class members write down the average time (in hours, to the nearest half-hour) they sleep per night.
William Reply
how we make a classes of this(170.3,173.9,171.3,182.3,177.3,178.3,174.175.3)
Sarbaz
6.5
phoenix
11
Shakir
7.5
Ron
why is always lower class bundry used
Caleb
Assume you are in a class where quizzes are 20% of your grade, homework is 20%, exam _1 is 15%,exam _2 is 15%, and the final exam is 20%.Suppose you are in the fifth week and you just found out that you scored a 58/63 on the fist exam. You also know that you received 6/9,8/10,9/9 on the first
Diamatu Reply
quizzes as well as a 9/11,10/10,and 4.5/7 on the first three homework assignment. what is your current grade in the course?
Diamatu
the answer is 2.6
Abdul

Get the best Introductory statistics course in your pocket!





Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask