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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

The information is given as, 30% of customers shopping at SHOPNO will switch to DAILY SHOPPING every month on the other hand 40% of customers shopping at DAILY SHOPPING will switch to other every month. What is the probability that customers will switch from A to B for next two months?
sharmin Reply
Calculate correlation coefficient, where SP(xy) = 144; SS(x) = 739; SS(y) = 58. (2 Points)
Ashfat Reply
The information are given from a randomly selected sample of age of COVID-19 patients who have already survived. These information are collected from 200 persons. The summarized information are as, n= 20; ∑x = 490; s^2 = 40. Calculate 95% confident interval of mean age.
Ashfat
The mode of the density of power of signal is 3.5. Find the probability that the density of a random signal will be more than 2.5.
Ashfat
The average time needed to repair a mobile phone set is 2 hours. If a customer is in queue for half an hour, what is the probability that his set will be repaired within 1.6 hours?
Ashfat
A quality control specialist took a random sample of n = 10 pieces of gum and measured their thickness and found the mean 9 and variance 0.04. Do you think that the mean thickness of the spearmint gum it produces is 8.4
nazrul Reply
3. The following are the number of mails received in different days by different organizations: Days (x) : 23, 35, 38, 50, 34, 60, 41, 32, 53, 67. Number of mails (y) : 18, 40, 52, 45, 32, 55, 50, 48, 26, 25. i) Fit a regression line of y on x and test the significance of regression. ii) Estimate y
Atowar Reply
The number of problem creating computers of two laboratories are as follows: Number of computers: 48, 6, 10, 12, 30, 11, 49, 17, 10, 14, 38, 25, 15, 19, 40, 12. Number of computers: 12, 10, 26, 11, 42, 11, 13, 12, 18, 5, 14, 38. Are the two laboratories similar in respect of problem creating compute
Tamim Reply
Is the severity of the drug problem in high school the same for boys and girls? 85 boys and 70 girls were questioned and 34 of the boys and 14 of the girls admitted to having tried some sort of drug. What can be concluded at the 0.05 level?
Ashfat Reply
null rejected
Pratik
a quality control specialist took a random sample of n=10 pieces of gum and measured their thickness and found the mean 7.6 and standered deviation 0.10. Do you think that the mean thickness of the spearmint gum it produces is 7.5?
Shanto Reply
99. A one sample, one-tail t-test is conducted and the test statistic value is calculated to be 2.56. The degrees of freedom for the test are 10. Which of the following conclusions for the test would be correct? a
Niaz Reply
A one sample, one-tail t-test is conducted and the test statistic value is calculated to be 2.56. The degrees of freedom for the test are 10. Which of the following conclusions for the test would be correct?
Niaz
what is null Hypothesis
Niaz
what is null Hypothesis
Niaz
when median is greater than mode?
Hafiza Reply
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Amaano
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Worthy
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oh
Worthy
when tail is positive
Jungjoon
define hypothesis
Worthy
I'm struggling to type it's on my laptop...statistics
Yoliswa
types of averages .mean median mode quarantiles MCQ question
Rupa Reply
what a consider data?
JAGESH Reply
Out of 25 students, 15 are male. Is the overall proportion of male students 0.7 in AIUB? (4 Points)
Omer Reply
15/25=0.6 or 60% standard calculation
Andrea
A quality control specialist took a random sample of n = 10 pieces of gum and measured their thickness and found the mean 7.6 and variance 0.01. Do you think that the mean thickness of the spearmint gum it produces is 7.5? (4 Points)
Omer
10 gums mean = 7.6 variance= 0.01 standard deviation= ? what us the data set?
Andrea
0.6
Rubina
A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Twelve older adults (over the age of 50) and twelve younger adults (between 20 and 40) were given a life satisfaction tes
Carlo Reply
how is it quantitative discrete data
Chinenye Reply
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Arifur Reply

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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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