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31 . The domain of X = {1, 2, 3, 4, 5, 6, 7, 8., 9, 10, 11, 12…27}. Because you are drawing without replacement, and 26 of the 52 cards are red, you have to draw a red card within the first 17 draws.

32 . X ~ G (0.24)

33 . μ =   1 p =   1 0.27 = 3.70

34 . σ =   1 p p 2 =   1 0.27 0.27 2 = 3.16

4.5: hypergeometric distribution

35 . Yes, because you are sampling from a population composed of two groups (boys and girls), have a group of interest (boys), and are sampling without replacement (hence, the probabilities change with each pick, and you are not performing Bernoulli trials).

36 . The group of interest is the cards that are spades, the size of the group of interest is 13, and the sample size is five.

4.6: poisson distribution

37 . A Poisson distribution models the number of events occurring in a fixed interval of time or space, when the events are independent and the average rate of the events is known.

38 . X ~ P (4)

39 . The domain of X = {0, 1, 2, 3, …..) i.e., any integer from 0 upwards.

40 . μ = 4
σ = 4 = 2

5.1: continuous probability functions

41 . The discrete variables are the number of books purchased, and the number of books sold after the end of the semester. The continuous variables are the amount of money spent for the books, and the amount of money received when they were sold.

42 . Because for a continuous random variable, P ( x = c ) = 0, where c is any single value. Instead, we calculate P ( c < x < d ), i.e., the probability that the value of x is between the values c and d .

43 . Because P ( x = c ) = 0 for any continuous random variable.

44 . P ( x >5) = 1 – 0.35 = 0.65, because the total probability of a continuous probability function is always 1.

45 . This is a uniform probability distribution. You would draw it as a rectangle with the vertical sides at 0 and 20, and the horizontal sides at 1 10 and 0.

46 . P ( 0   < x < 4 ) = ( 4 0 ) ( 1 10 ) =   0.4

5.2: the uniform distribution

47 . P ( 2   < x < 5 ) = ( 5 2 ) ( 1 10 ) =   0.3

48 . X ~ U (0, 15)

49 . f ( x ) = 1 b a for ( a x b )  so  f ( x ) = 1 30 for ( 0 x 30 )

50 . μ =   a + b 2 =   0 + 30 5 = 15.0
σ =   ( b a ) 2 12 =   ( 30 0 ) 2 12 = 8.66

51 . P ( x < 10 ) = ( 10 ) ( 1 30 ) =   0.33

5.3: the exponential distribution

52 . X has an exponential distribution with decay parameter m and mean and standard deviation 1 m . In this distribution, there will be a relatively large numbers of small values, with values becoming less common as they become larger.

53 . μ = σ = 1 m = 1 10 = 0.1

54 . f ( x ) = 0.2 e –0.2 x where x ≥ 0.

6.1: the standard normal distribution

55 . The random variable X has a normal distribution with a mean of 100 and a standard deviation of 15.

56 . X ~ N (0,1)

57 . z = x μ σ so z = 112 109 4.5 = 0.67

58 . z = x μ σ so z = 100 109 4.5 = 2.00

59 .   z = 105 109 4.5 = −0.89
This girl is shorter than average for her age, by 0.89 standard deviations.

60 . 109 + (1.5)(4.5) = 115.75 cm

61 . We expect about 68 percent of the heights of girls of age five years and zero months to be between 104.5 cm and 113.5 cm.

62 . We expect 99.7 percent of the heights in this distribution to be between 95.5 cm and 122.5 cm, because that range represents the values three standard deviations above and below the mean.

6.2: using the normal distribution

63 . Yes, because both np and nq are greater than five.
np = (500)(0.20) = 100 and nq = 500(0.80) = 400

Questions & Answers

What is the variances of 568
Helen Reply
what u asking...
friend
what variance would have a single value..?
friend
variance happened only in a group of values..
friend
if we have a group of values...1st we find its average..ie..'mean'..then we calculate each value's difeerence from the mean..then we will square each 'difference value'.then we devide total of sqared value by n or n-1..that is what variance...
friend
What is the variances of 258
Helen Reply
66,564
Mampy
what is the sample size if the degree of freedom is 25?
Arthur Reply
26..
friend
25
Tariku
27
Tariku
degrees of freedom may differ with respect to distribution...so tell which distribution you have selected...?
friend
my distribution is 27
Tariku
how to understand statistics
Edwin Reply
you are working for a bank.The bank manager wants to know the mean waiting time for all customers who visit this bank. she has asked you to estimate this mean by taking a sample . Briefly explain how you will conduct this study. assume the data set on waiting times for 10 customers who visit a bank. Then estimate the population mean. choose your own confidence level.
Halpha Reply
what marriage for 10 years
Ambaye Reply
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab Reply
how can we find the expectation of any function of X?
Jennifer
I've been using this app for some time now. I'm taking a stats class in college in spring and I still have no idea what's going on. I'm also 55 yrs old. Is there another app for people like me?
Tamala
Serious
Hamza
yes I am. it's been decades since I've been in school.
Tamala
who are u
zaheer
is there a private chat we can do
Tamala
hello how can I get PDF of solutions introduction mathematical statistics ( fourth education) who can help me
ahssal
can anyone help me
Halim
what is probability
zaheer Reply
simply probability means possibility.. definition:Probability is a measure of the likelihood of an event to occur.
laraib
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab
classification of data by attributes is called
Yamin Reply
qualitative classification
talal
tell me details about measure of Dispersion
Halim
Following data provided Class Frequency less than 10 10-20 5 15 10-30 25 12 40 and above Which measure of central tendency would you compute and why?
Nija Reply
a box contains a few red and a few blue balls.one ball is drawn randomly find the probability of getting a red ball if we know that there are 30 red and 40 blue balls in the box
harish Reply
3/7
RICH
Total=30+40=70 P(red balls) =30/70 Therefore the answer is 3/7
Anuforo
define transport statistical unit
Dennis Reply
describe each transport statistical unit
Dennis
explain uses of each transport statistical unit
Dennis
identify various transport statistical units with their example
Dennis
I didn't understand about Chi- square.
Esayas Reply
explain the concept of data analysis and data processing
Kim Reply
the following data represent the number of pop up advertisement received by 10 families during the past month.calculate the mean number of advertisement received by each family during month.43,37,35,30,41,23,33,31,16,21
ejaz Reply
mean=43+37+35+30+41+23+33+31+16/10 =310/10 =31
Anuforo
43+37+35+30+41+23+33+31+16 divided by 10 =310/10 =31
Anuforo
=310/10 =31
Anuforo

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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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