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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 Confidence Interval
ala Reply
sample mean 25, sample standard deviation 20, sample size 200, calculate the confidence interval using the given values and the original confidence level of 90%.
Cady Reply
Can you help me in mathematical statistics problems?
bint-e-taj Reply
yes
Kc
Pls who can help me to teach me statistics
nasir
i need tutor for statistics plz
Rana
ok
Ekene
the power of the test is
Ejaz Reply
please can anyone help me solve these questions below? I need help please.
MMSI
a)An investor wants to eliminate seven of the investments in her portfolio by selling 4 stocks and 3 bonds. In how many can these be sold if among 25 securities in the portfolio,13 are stocks and the rest bonds?
MMSI
a)If a random variable has the standard normal distribution,what are the probabilities that it will take on a value: i)Less than 1.64 ii)Greater than-0.47
MMSI
b)A random variable has a normal distribution with a mean of 60 and standard deviation 5.2.What are the probabilities that the random variable will take on a value: i)Less than 65.2 ii)Between 48 and 72?
MMSI
b)If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001,use the Poisson law to calculate the probability that out of 2000 individuals i)Exactly 3 individuals will suffer a bad reaction. ii)More than 2 individuals will suffer a bad reaction.
MMSI
b)The breakfast menu serve data popular 5-star Hotel in Accra consists of the following items: Juice-Mango,Grape,Apple. Toast-Whitewheat,Whole wheat. Egg:Fried,Hard-boiled,Scrambled. Beverage:Coffee,Tea,Cocoa.
MMSI
Continuation of the last question.Assist the Hotel manager to determine the number of possible breakfast combinations that can be served, one from each category
MMSI
please I need help.
MMSI
3x2x3
Vince
Are you answering the last question?
MMSI
please you guys should help me I need it so badly
MMSI
bias came in sampling due to
Muzammil Reply
sampling error
Vikram
what is the difference between population and sample
Inam
Sample is the group of individual who participate in your study. Sample is a subset of population. Population is the broader group of people to whom you intend to generalize the results of your study.
Ekene
how do you find z if you only know the area of .0808
Cady Reply
construct a frequency distribution
Sana
How to take a random sample of 30 observations
Hamna Reply
you can use the random function to generate 30 numbers or observation
smita
How we can calculate chi-square if observed x٫y٫z/frequency 40,30,20 Total/90
Insha Reply
calculate chi-square if observed x,y,z frequency 40,30,20total 90
Insha
find t value,if boysN1, ،32,M1,87.43 S1square,39.40.GirlsN2,34,M2,82.58S2square,40.80 Determine whether the results are significant or insignificant
Insha
The heights of a random sample of 100 entering HRM Freshman of a certain college is 157 cm with a standard deviation of 8cm. test the data against the claim that the overall height of all entering HRM students is 160 cm. previous studies showed that
Crispen Reply
complete the question.. as data given N = 100,mean= 157 cm, std dev = 8 cm..
smita
Z=x-mu/ std dev
smita
the power of the test is
Ejaz
find the mean of 25,26,23,25,45,45,58,58,50,25
Asmat Reply
add all n divide by 10 i.e 38
smita
38
hhaa
amit
1 . The “average increase” for all NASDAQ stocks is the:
Jamshaid Reply
STATISTICS IN PRACTICE: This is a group assignment that seeks to reveal students understanding of statistics in general and it’s practical usefulness. The following are the guidelines; 1.      Each group has to identify a natural process or activity and gather data about/from the process. 2.     
Kofi Reply
The diameter of an electric cable,say, X is assumed to be continoues random variable with p.d.f f(x)=6x(1-x); ≤x≤1 a)check that f(X) is p.d.f b) determine a number b such that p(Xb)
Syed Reply
A manufacturer estimate 3% of his output is defective. Find the probability that in a sample of 10 items (a) less than two will be defective (b) more than two will be defective.
ISAIAH Reply
A manufacturer estimates that 3% of his output of a small item is defective. Find the probabilities that in a sample of 10 items (a) less than two and (b) more than two items will be defective.
ISAIAH
use binomial distribution with parameter n=10, p= 0.03, q=0.97
Shivprasad
the standard deviation of a symmetrical distribution is 7.8 . what must be the value of forth moment about the mean in order that distribution be a) leptokurtic b) mesokurtic c) platy kyrtic intrept the obtain value of a b and c
Tushar 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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