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64 . μ = n p = ( 500 ) ( 0.20 ) = 100
σ = n p q = 500 ( 0.20 ) ( 0.80 ) = 8.94

65 . Fifty percent, because in a normal distribution, half the values lie above the mean.

66 . The results of our sample were two standard deviations below the mean, suggesting it is unlikely that 20 percent of the lotto tickets are winners, as claimed by the distributor, and that the true percent of winners is lower. Applying the Empirical Rule, If that claim were true, we would expect to see a result this far below the mean only about 2.5 percent of the time.

7.1: the central limit theorem for sample means (averages)

67 . The central limit theorem states that if samples of sufficient size drawn from a population, the distribution of sample means will be normal, even if the distribution of the population is not normal.

68 . The sample size of 30 is sufficiently large in this example to apply the central limit theorem. This theorem ] states that for samples of sufficient size drawn from a population, the sampling distribution of the sample mean will approach normality, regardless of the distribution of the population from which the samples were drawn.

69 . You would not expect each sample to have a mean of 50, because of sampling variability. However, you would expect the sampling distribution of the sample means to cluster around 50, with an approximately normal distribution, so that values close to 50 are more common than values further removed from 50.

70 . X ¯ N ( 25 , 0.2 ) because X ¯ N ( μ x , σ x n )

71 . The standard deviation of the sampling distribution of the sample means can be calculated using the formula ( σ x n ) , which in this case is ( 16 50 ) . The correct value for the standard deviation of the sampling distribution of the sample means is therefore 2.26.

72 . The standard error of the mean is another name for the standard deviation of the sampling distribution of the sample mean. Given samples of size n drawn from a population with standard deviation σ x , the standard error of the mean is ( σ x n ) .

73 . X ~ N (75, 0.45)

74 . Your friend forgot to divide the standard deviation by the square root of n .

75 . z =   x ¯   μ x σ x =   76 75 4.5 = 2.2

76 . z = x ¯   μ x σ x =   74.7 75 4.5 = −0.67

77 . 75 + (1.5)(0.45) = 75.675

78 . The standard error of the mean will be larger, because you will be dividing by a smaller number. The standard error of the mean for samples of size n = 50 is:
( σ x n ) =   4.5 50 = 0.64

79 . You would expect this range to include values up to one standard deviation above or below the mean of the sample means. In this case:
70 + 9 60 = 71.16 and 70 9 60 = 68.84 so you would expect 68 percent of the sample means to be between 68.84 and 71.16.

80 . 70 + 9 100 = 70.9 and 70 9 100 = 69.1 so you would expect 68 percent of the sample means to be between 69.1 and 70.9. Note that this is a narrower interval due to the increased sample size.

7.2: the central limit theorem for sums

81 . For a random variable X , the random variable ΣX will tend to become normally distributed as the size n of the samples used to compute the sum increases.

82 . Both rules state that the distribution of a quantity (the mean or the sum) calculated on samples drawn from a population will tend to have a normal distribution, as the sample size increases, regardless of the distribution of population from which the samples are drawn.

Questions & Answers

describe the methods of calculation of sample
Anuradha Reply
what are the various uses of statistics in education
Buhari Reply
Survey, Public allocation of federal funds, business analysis and consumer data, the lotto, government programs and special services.
Willard
probability sampling
Rosy Reply
dicuss probability sampling
Rosy
given that a sample is normally distributed with M=10 sd=8 determine
Rosy
disscuss probability sampling
Rosy
Discuss probability sampling
Rosy
What is mean
Rosy
Probability sampling is based on the fact that every member of a population has a known and equal chance of being selected. For example, if you had a population of 100 people, each person would have odds of 1 out of 100 of being chosen. With non-probability sampling, those odds are not equal.
Willard
The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.  To calculate it:  • add up all the numbers, • then divide by how many numbers there are. Example: what is the mean of 2, 7 and 9? Add the numbers: 2 + 7 + 9 = 18 Divide by how many numbers, 3 you
Willard
get 6
Willard
guidelines of designing a table
Anuradha
you can find that information on this website there is a lot of information. It's about interpreting what the concept of information & data you are getting from the graph and understanding how to read the graph and analyze the information. ***understandinggraphics.com/design/data-table-design/
Willard
find X and Y so that the ordered data set has a mean of 38 and median of 35 17, 22, 26, 29, 34, X, 42, 67 , 70, Y
Mohamed
Frequency find questions
Rimsha Reply
?
Rosy
What is nominal variable
olusola Reply
Write short notes on, nominal variable, ordinal variable, internal variable, ratio variable.
olusola
P( /x-50/ less than or equal to 5 ) where mean =52 and Variance =25
Jay Reply
how I get the mcq
Mukesh Reply
please what is data mining
Josephine Reply
the exploration and analysis of large data to discover meaningful patterns and rules
Hussein
how do we calculate the median
All Reply
f(x)=cx(1-x)^4 as x range 4rm 0<=x<=1. Can someone pls help me find d constant C. By integration only..
Akeem Reply
uses of statistics in Local Government
Saleema Reply
Hi
Tamuno
hello
Saleema
state road transport corporation
Atul
District statistical officer
Atul
statistical services
Atul
Please is this part of the IMT program
Tamuno
testing of drugs
Shambhavi
hii 2
Qamar-ul-
How about population census
Tamuno
Hello every one
Okoi
sample survey is done by local government in each and every field.
syeda
statistics is used in almost every government organisations such as health department, economic department, census, weather forecasting fields
raghavendra
that's true
syeda
statistics is one of the tool that represents the falling and rising of any cases in one sheet either that is in population census whether forecast as well as economic growth
Aadil
statistic is a technique, and statistics is a subject
syeda
what is business statistics
PM Reply
Probability tells you the likelihood of an event happening. ... The higher the probability, the more likely it is to happen. Probability is a number or fraction between 0 and 1. A probability of 1 means something will always happen, and a probability of 0 means something will never happen...
La Reply
Saying it's a number between zero and one means it is a fraction so you could remove "or fraction" from you definition.
Carlos
wouldn't be correct to remove fractions, saying a number is justified as probabilities can also be decimals between 0 and 1.
Denzel
Saying "a number" will include it being a decimal which are themselves fractions in another form.
Carlos
I will simply say a probability is a number in the range zero to one, inclusive.
Carlos
f#$
Carlos
How to delete an entry? This last one was a pocket print.
Carlos
what is probability
sky-D Reply
chance of occurrence
Sikander
what is data
Muhd Reply
raw facts and figures
Sikander
information of any kind
Tahir

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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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