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89 . Applying the law of large numbers, which sample mean would expect to be closer to the population mean, a sample of size ten or a sample of size 100?

Use this information for the next three questions. A manufacturer makes screws with a mean diameter of 0.15 cm (centimeters) and a range of 0.10 cm to 0.20 cm; within that range, the distribution is uniform.

90 . If X = the diameter of one screw, what is the distribution of X ?

91 . Suppose you repeatedly draw samples of size 100 and calculate their mean. Applying the central limit theorem, what is the distribution of these sample means?

92 . Suppose you repeatedly draw samples of 60 and calculate their sum. Applying the central limit theorem, what is the distribution of these sample sums?

Practice test 2 solutions

Probability distribution function (pdf) for a discrete random variable

1 . The domain of X = {English, Mathematics,….], i.e., a list of all the majors offered at the university, plus “undeclared.”

2 . The domain of Y = {0, 1, 2, …}, i.e., the integers from 0 to the upper limit of classes allowed by the university.

3 . The domain of Z = any amount of money from 0 upwards.

4 . Because they can take any value within their domain, and their value for any particular case is not known until the survey is completed.

5 . No, because the domain of Z includes only positive numbers (you can’t spend a negative amount of money). Possibly the value –7 is a data entry error, or a special code to indicated that the student did not answer the question.

6 . The probabilities must sum to 1.0, and the probabilities of each event must be between 0 and 1, inclusive.

7 . Let X = the number of books checked out by a patron.

8 . P ( x >2) = 0.10 + 0.05 = 0.15

9 . P ( x ≥ 0) = 1 – 0.20 = 0.80

10 . P ( x ≤ 3) = 1 – 0.05 = 0.95

11 . The probabilities would sum to 1.10, and the total probability in a distribution must always equal 1.0.

12 . x ¯ = 0(0.20) + 1(0.45) + 2(0.20) + 3(0.10) + 4(0.05) = 1.35

Mean or expected value and standard deviation

13 .

x P ( x ) x P ( x )
30 0.33 9.90
40 0.33 13.20
60 0.33 19.80

14 . x ¯ = 9.90 + 13.20 + 19.80 = 42.90

15 . P ( x = 30) = 0.33
P ( x = 40) = 0.33
P ( x = 60) = 0.33

16 .

x P ( x ) xP ( x ) ( x μ ) 2 P ( x )
30 0.33 9.90 (30 – 42.90) 2 (0.33) = 54.91
40 0.33 13.20 (40 – 42.90) 2 (0.33) = 2.78
60 0.33 19.90 (60 – 42.90) 2 (0.33) = 96.49

17 . σ x = 54.91 + 2.78 + 96.49 = 12.42

Binomial distribution

18 . q = 1 – 0.65 = 0.35

19 .

  1. There are a fixed number of trials.
  2. There are only two possible outcomes, and they add up to 1.
  3. The trials are independent and conducted under identical conditions.

20 . No, because there are not a fixed number of trials

21 . X ~ B (100, 0.65)

22 . μ = np = 100(0.65) = 65

23 . σ x = n p q = 100 ( 0.65 ) ( 0.35 ) = 4.77

24 . X = Joe gets a hit in one at-bat (in one occasion of his coming to bat)

25 . X ~ B (20, 0.4)

26 . μ = np = 20(0.4) = 8

27 . σ x = n p q = 20 ( 0.40 ) ( 0.60 ) = 2.19

4.4: geometric distribution

28 .

  1. A series of Bernoulli trials are conducted until one is a success, and then the experiment stops.
  2. At least one trial is conducted, but there is no upper limit to the number of trials.
  3. The probability of success or failure is the same for each trial.

29 . T T T T H

30 . The domain of X = {1, 2, 3, 4, 5, ….n}. Because you are drawing with replacement, there is no upper bound to the number of draws that may be necessary.

Questions & Answers

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
if putting y=3x examine that correlation coefficient between x and y=3x is 1.
Aadrsh 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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