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References

“Blood Pressure of Males and Females.” StatCruch, 2013. Available online at http://www.statcrunch.com/5.0/viewreport.php?reportid=11960 (accessed May 14, 2013).

“The Use of Epidemiological Tools in Conflict-affected populations: Open-access educational resources for policy-makers: Calculation of z-scores.” London School of Hygiene and Tropical Medicine, 2009. Available online at http://conflict.lshtm.ac.uk/page_125.htm (accessed May 14, 2013).

“2012 College-Bound Seniors Total Group Profile Report.” CollegeBoard, 2012. Available online at http://media.collegeboard.com/digitalServices/pdf/research/TotalGroup-2012.pdf (accessed May 14, 2013).

“Digest of Education Statistics: ACT score average and standard deviations by sex and race/ethnicity and percentage of ACT test takers, by selected composite score ranges and planned fields of study: Selected years, 1995 through 2009.” National Center for Education Statistics. Available online at http://nces.ed.gov/programs/digest/d09/tables/dt09_147.asp (accessed May 14, 2013).

Data from the San Jose Mercury News .

Data from The World Almanac and Book of Facts .

“List of stadiums by capacity.” Wikipedia. Available online at https://en.wikipedia.org/wiki/List_of_stadiums_by_capacity (accessed May 14, 2013).

Data from the National Basketball Association. Available online at www.nba.com (accessed May 14, 2013).

Chapter review

A z -score is a standardized value. Its distribution is the standard normal, Z ~ N (0, 1). The mean of the z -scores is zero and the standard deviation is one. If z is the z -score for a value x from the normal distribution N ( µ , σ ) then z tells you how many standard deviations x is above (greater than) or below (less than) µ .

Formula review

Z ~ N (0, 1)

z = a standardized value ( z -score)

mean = 0; standard deviation = 1

To find the K th percentile of X when the z -scores is known:
k = μ + ( z ) σ

z -score: z = x  –  μ σ

Z = the random variable for z -scores

Z ~ N (0, 1)

A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X in words. X = ____________.

ounces of water in a bottle

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A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?

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X ~ N (1, 2)

σ = _______

2

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A company manufactures rubber balls. The mean diameter of a ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X = ______________.

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X ~ N (–4, 1)

What is the median?

–4

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X ~ N (3, 5)

σ = _______

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X ~ N (–2, 1)

μ = _______

–2

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What does a z -score measure?

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What does standardizing a normal distribution do to the mean?

The mean becomes zero.

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Is X ~ N (0, 1) a standardized normal distribution? Why or why not?

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What is the z -score of x = 12, if it is two standard deviations to the right of the mean?

z = 2

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What is the z -score of x = 9, if it is 1.5 standard deviations to the left of the mean?

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What is the z -score of x = –2, if it is 2.78 standard deviations to the right of the mean?

z = 2.78

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What is the z -score of x = 7, if it is 0.133 standard deviations to the left of the mean?

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Suppose X ~ N (2, 6). What value of x has a z -score of three?

x = 20

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Suppose X ~ N (8, 1). What value of x has a z -score of –2.25?

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Suppose X ~ N (9, 5). What value of x has a z -score of –0.5?

x = 6.5

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Suppose X ~ N (2, 3). What value of x has a z -score of –0.67?

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Suppose X ~ N (4, 2). What value of x is 1.5 standard deviations to the left of the mean?

x = 1

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Suppose X ~ N (4, 2). What value of x is two standard deviations to the right of the mean?

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Suppose X ~ N (8, 9). What value of x is 0.67 standard deviations to the left of the mean?

x = 1.97

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Suppose X ~ N (–1, 2). What is the z -score of x = 2?

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Suppose X ~ N (12, 6). What is the z -score of x = 2?

z = –1.67

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Suppose X ~ N (9, 3). What is the z -score of x = 9?

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Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z -score of x = 5.5?

z ≈ –0.33

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In a normal distribution, x = 5 and z = –1.25. This tells you that x = 5 is ____ standard deviations to the ____ (right or left) of the mean.

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In a normal distribution, x = 3 and z = 0.67. This tells you that x = 3 is ____ standard deviations to the ____ (right or left) of the mean.

0.67, right

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In a normal distribution, x = –2 and z = 6. This tells you that x = –2 is ____ standard deviations to the ____ (right or left) of the mean.

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In a normal distribution, x = –5 and z = –3.14. This tells you that x = –5 is ____ standard deviations to the ____ (right or left) of the mean.

3.14, left

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In a normal distribution, x = 6 and z = –1.7. This tells you that x = 6 is ____ standard deviations to the ____ (right or left) of the mean.

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About what percent of x values from a normal distribution lie within one standard deviation (left and right) of the mean of that distribution?

about 68%

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About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution?

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About what percent of x values lie between the second and third standard deviations (both sides)?

about 4%

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Suppose X ~ N (15, 3). Between what x values does 68.27% of the data lie? The range of x values is centered at the mean of the distribution (i.e., 15).

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Suppose X ~ N (–3, 1). Between what x values does 95.45% of the data lie? The range of x values is centered at the mean of the distribution(i.e., –3).

between –5 and –1

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Suppose X ~ N (–3, 1). Between what x values does 34.14% of the data lie?

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About what percent of x values lie between the mean and three standard deviations?

about 50%

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About what percent of x values lie between the mean and one standard deviation?

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About what percent of x values lie between the first and second standard deviations from the mean (both sides)?

about 27%

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About what percent of x values lie betwween the first and third standard deviations(both sides)?

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Use the following information to answer the next two exercises: The life of Sunshine CD players is normally distributed with 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.

Define the random variable X in words. X = _______________.

The lifetime of a Sunshine CD player measured in years.

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Questions & Answers

the diagram of the digestive system
Assiatu Reply
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
what is cell divisoin?
Aron Reply
Diversity of living thing
ISCONT
what is cell division
Aron Reply
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
What is life?
Allison Reply
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
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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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