# 6.2 Using the normal distribution  (Page 4/25)

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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)

What is the area to the right of one?

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

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

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

What is the area to the right of three?

1 – P ( x <3) or P ( x >3)

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

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

Use the following information to answer the next four exercises:

X ~ N (54, 8)

Find the probability that x >56.

Find the probability that x <30.

0.0013

Find the 80 th percentile.

Find the 60 th percentile.

56.03

X ~ N (6, 2)

Find the probability that x is between three and nine.

X ~ N (–3, 4)

Find the probability that x is between one and four.

0.1186

X ~ N (4, 5)

Find the maximum of x in the bottom quartile.

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.
2. P (0< x <____________) = ___________ (Use zero for the minimum value of x .)
1. Check student’s solution.
2. 3, 0.1979

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.
2. P (__________< x <__________) = __________

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%.
2. P ( x < k ) = __________ Therefore, k = _________
1. Check student’s solution.
2. 0.70, 4.78 years

#### Questions & Answers

what is the sample size if the degree of freedom is 25?
Arthur Reply
26..
friend
how to understand statistics
Edwin Reply
you are working for a bank.The bank manager wants to know the mean waiting time for all customers who visit this bank. she has asked you to estimate this mean by taking a sample . Briefly explain how you will conduct this study. assume the data set on waiting times for 10 customers who visit a bank. Then estimate the population mean. choose your own confidence level.
Halpha Reply
what marriage for 10 years
Ambaye Reply
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab Reply
how can we find the expectation of any function of X?
Jennifer
I've been using this app for some time now. I'm taking a stats class in college in spring and I still have no idea what's going on. I'm also 55 yrs old. Is there another app for people like me?
Tamala
Serious
Hamza
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zaheer
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Tamala
hello how can I get PDF of solutions introduction mathematical statistics ( fourth education) who can help me
ahssal
can anyone help me
Halim
what is probability
zaheer Reply
simply probability means possibility.. definition:Probability is a measure of the likelihood of an event to occur.
laraib
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab
classification of data by attributes is called
Yamin Reply
qualitative classification
talal
tell me details about measure of Dispersion
Halim
Following data provided Class Frequency less than 10 10-20 5 15 10-30 25 12 40 and above Which measure of central tendency would you compute and why?
Nija Reply
a box contains a few red and a few blue balls.one ball is drawn randomly find the probability of getting a red ball if we know that there are 30 red and 40 blue balls in the box
harish Reply
3/7
RICH
Total=30+40=70 P(red balls) =30/70 Therefore the answer is 3/7
Anuforo
define transport statistical unit
Dennis Reply
describe each transport statistical unit
Dennis
explain uses of each transport statistical unit
Dennis
identify various transport statistical units with their example
Dennis
I didn't understand about Chi- square.
Esayas Reply
explain the concept of data analysis and data processing
Kim Reply
the following data represent the number of pop up advertisement received by 10 families during the past month.calculate the mean number of advertisement received by each family during month.43,37,35,30,41,23,33,31,16,21
ejaz Reply
mean=43+37+35+30+41+23+33+31+16/10 =310/10 =31
Anuforo
43+37+35+30+41+23+33+31+16 divided by 10 =310/10 =31
Anuforo
=310/10 =31
Anuforo
the following data represent the number of pop up advertisement received by 10 families during the past month.calculate the mean number of advertisement received by each family during month.43,37,35,30,41,23,33,31,16,21
ejaz Reply
In a recent survey of nurses in Region II, it was found out that the average monthly net income of nurses is Php 8,048.25. Suppose a researcher wants to test this figure by taking a random sample of 158 nurses in Region II to determine whether the monthly income has changed. Supposed further that th
Sweet Reply

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