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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 standard deviation?
Jawed Reply
It is the measure of the variation of certain values from the Mean (Center) of a frequency distribution of sample values for a particular Variable.
Dominic
Yeah....the simplest one
IRFAN
what is the number of x
Godgift Reply
10
Elicia
Javed Arif
Jawed
how will you know if a group of data set is a sample or population
Kingsley Reply
population is the whole set and the sample is the subset of population.
umair
if the data set is drawn out of a larger set it is a sample and if it is itself the whole complete set it can be treated as population.
Bhavika
hello everyone if I have the data set which contains measurements of each part during 10 years, may I say that it's the population or it's still a sample because it doesn't contain my measurements in the future? thanks
Alexander
Pls I hv a problem on t test is there anyone who can help?
Peggy
What's your problem Peggy Abang
Dominic
Bhavika is right
Dominic
what is the problem peggy?
Bhavika
hi
Sandeep
Hello
adeagbo
hi
Bhavika
hii Bhavika
Dar
Hi eny population has a special definition. if that data set had all of characteristics of definition, that is population. otherwise that is a sample
Hoshyar
three coins are tossed. find the probability of no head
Kanwal Reply
three coins are tossed consecutively or what ?
umair
p(getting no head)=1/8
umair
or .125 is the probability of getting no head when 3 coins are tossed
umair
🤣🤣🤣
Simone
what is two tailed test
Umar Reply
if the diameter will be greater than 3 cm then the bullet will not fit in the barrel of the gun so you are bothered for both the sides.
umair
in this test you are worried on both the ends
umair
lets say you are designing a bullet for thw gun od diameter equals 3cm.if the diameter of the bullet is less than 3 cm then you wont be able to shoot it
umair
In order to apply weddles rule for numerical integration what is minimum number of ordinates
Anjali Reply
excuse me?
Gabriel
why?
Tade
didn't understand the question though.
Gabriel
which question? ?
Tade
We have rules of numerical integration like Trapezoidal rule, Simpson's 1/3 and 3/8 rules, Boole's rule and Weddle rule for n =1,2,3,4 and 6 but for n=5?
John
geometric mean of two numbers 4 and 16 is:
iphone Reply
10
umair
really
iphone
quartile deviation of 8 8 8 is:
iphone
sorry 8 is the geometric mean of 4,16
umair
quartile deviation of 8 8 8 is
iphone
can you please expalin the whole question ?
umair
mcq
iphone
h
iphone
can you please post the picture of that ?
umair
how
iphone
hello
John
10 now
John
how to find out the value
srijth Reply
can you be more specific ?
umair
yes
KrishnaReddy
what is the difference between inferential and descriptive statistics
Eze Reply
descriptive statistics gives you the result on the the data like you can calculate various things like variance,mean,median etc. however, inferential stats is involved in prediction of future trends using the previous stored data.
umair
if you need more help i am up for the help.
umair
Thanks a lot
Anjali
Inferential Statistics involves drawing conclusions on a population based on analysis of a sample. Descriptive statistics summarises or describes your current data as numerical calculations or graphs.
fred
my pleasure😊. Helping others offers me satisfaction 😊
umair
for poisson distribution mean............variance.
mehul Reply
both are equal to mu
Faizan
mean=variance
Faizan
what is a variable
Bonolo Reply
something that changes
Festus
why we only calculate 4 moment of mean? asked in papers.
Faizan Reply
why we only 4 moment of mean ? asked in BA exam
Faizan
Good evening, can you please help me by sharing regression and correlation analysis notes....thank you in advance
Refiloe Reply
Hello, can you please share the possible questions that are likely to be examined under the topic: regression and correlation analysis.
Refiloe
for normal distribution mean is 2 & variance is 4 find mu 4?
Faizan Reply
repeat quastion again
Yusuf
find mu 4. it can be wrong but want to prove how.
Faizan
for a normal distribution if mu 4 is 12 then find mu 3?
Faizan Reply
Question hi wrong ha
Tahir
ye BA mcqs me aya he teen he. 2dafa aya he
Faizan
if X is normally distributed. (n,b). then its mean deviation is?
Faizan
The answer is zero, because all odd ordered central moments of a normal distribution are Zero.
nikita
which question is zero
Faizan
sorry it is (5,16) in place of (n,b)
Faizan
I got. thanks. it is zero.
Faizan
a random variable having binomial distribution is?
Bokaho

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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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