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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

pls I need understand this statistics very will is giving me problem
Bolanle Reply
Sixty-four third year high school students were given a standardized reading comprehension test. The mean and standard deviation obtained were 52.27 and 8.24, respectively. Is the mean significantly different from the population mean of 50? Use the 5% level of significance.
Daryl Reply
No
Ariel
how do I find the modal class
Bruce Reply
look for the highest occuring number in the class
Kusi
the probability of an event occuring is defined as?
James Reply
The probability of an even occurring is expected event÷ event being cancelled or event occurring / event not occurring
Gokuna
what is simple bar chat
Toyin Reply
Simple Bar Chart is a Diagram which shows the data values in form of horizontal bars. It shows categories along y-axis and values along x-axis. The x-axis displays above the bars and y-axis displays on left of the bars with the bars extending to the right side according to their values.
Muhammad
statistics is percentage only
Moha Reply
the first word is chance for that we use percentages
muhammad
it is not at all that statistics is a percentage only
Shambhavi
I need more examples
Luwam Reply
how to calculate sample needed
Jim Reply
mole of sample/mole ratio or Va Vb
Gokuna
how to I solve for arithmetic mean
Joe Reply
Yeah. for you to say.
James
yes
niharu
how do I solve for arithmetic mean
Joe Reply
please answer these questions
niharu
add all the data and divide by the number of data sets. For example, if test scores were 70, 60, 70, 80 the total is 280 and the total data sets referred to as N is 4. Therfore the mean or arthritmatic average is 70. I hope this helps.
Jim
*Tan A - Tan B = sin(A-B)/CosA CosB ... *2sinQ/Cos 3Q = tan 3Q - tan Q
Ibraheem Reply
standard error of sample
Umar Reply
what is subjective probability
Avela Reply
how to calculate the Steadman rank correlation
David
what is sampling? i want to know about the definition of sampling.
anup Reply
what is sample...?
Abdul Reply
In terms of Statistics or Research , It is a subset of population for measurement.
Da

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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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