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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

what is the frequency
okoh Reply
Frequency is the number of all object which is comes from population or sample size
Faiqa
Denoted by f
Faiqa
number of all objects?
Amir
frequency is the rate of occurrence of an object
Leek
Explain nominal and ordinal variables
Oyinlola
 nominal variables are those variable which is used to “name,” a series of values.
Amir
while  ordinal scales provide good information about the order of choices,for example in a customer satisfaction survey.
Amir
what is the difference between Mean and Varience?
Amir
Sum of total object, divided by number of object is called mean
Faiqa
variance?
Amir
faiqa U didn't clear me.Sorry
Amir
what is df in statistics
Oyinlola
degre of freedom
Amir
Acquits the accused when in fact,he is ennocent
Barbie Reply
what is statistics
scholar Reply
statistics is a mathematical sciences which deals with collection,presentation and analysis the numerical data
CH
statistics is a tools who convert data into information
CH
method of collection of data
Abdul Reply
problems of find mean and standard deviation with drawing curve
Kukkuzz Reply
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

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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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