## (Solved) Assignment NO. 1 week2-week7 Student Full Name:___________________________________ . Student ID:__________________________________________ . CRN...

Section-I

State whether the following statements are True or False. (15 marks, 1 Mark Each)

• - The amount of milk that a cow produces in a gallon an example of continuous data. Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
• - Systematic Sampling is sampling in which data is obtained by selecting every kth object. Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
• - Any characteristic of a population distribution may properly be referred to as a parameter
• Â - Populations are always infinite.Â Â
• - The population mean and the population median will not generally be equal to one another. Â Â
• - There are four quartiles that divided the data into four equal parts. Â Â Â
• - The probability of an impossible event is one.
• - If A and B are disjoint events, then in conditional probabilityÂ Â Â Â Â Â Â Â Â Â Â Â
• - Mean value over an infinite number of observations of the variables is the expected value of random variables.
• - Poisson distribution is a continuous probability distribution.
• - In the standard normal distribution the standard deviation is always exactly zero.
• - The distribution of sample will as the sample size increases, approach a normal distribution.Â Â
• - A point estimate is a single value or point used to approximate a population parameter.Â
• - A critical value is a Z-score separating unlikely value from those that are likely to occur.
• - As the sample size increases, the sampling error will increase as well.

Section-II

Â (Multiple Choice Questions) Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (15 marks, 1 Mark Each)

• Â The subject in which college students major.
• Ordinal
• Nominal
• Ratio
• Interval
• Which one of the following variables is not categorical?
• The choice on a test item: true or false.
• Â The gender of a person: male or female
• Â The age in years of a person.
• Â Â TheÂ maritalÂ statusÂ ofÂ aÂ person:Â single,Â married,Â divorced,Â other.
• A distribution of data that is the left half of its histogram is roughly a mirror image of its right half called:
• SkewedÂ Â Â Â Â Â Â Â Â Â
• SymmetricÂ Â Â Â Â
• both a and b
• None
• A sample value that lies very far away from the majority of the other sample values is
• The center.
• A distribution.
• An outlier.
• aÂ variance.
• Which of the following are examples of a variable?
• Gender of a high school graduate.
• Number of major credit cards a person has.
• Type of automobile transmission.
• AllÂ ofÂ theÂ above.
• Which of the following is not a measure of variability?
• Variance.
• Standard deviation.
• Mean.
• Median.
• Â An urn contains 6 blue or white balls, 4 of them are blue, what is theÂ Â Â  probability of getting white ball?
• 0.7
• 1/3
• 3
• 1

What is the probability of rolling a die and getting either a 1 or a 6?

Â Â Â Â  a. 1/3

Â Â Â Â  b. 1/2

Â Â Â  c. 6/21

Â Â Â  d. 8/2

9. Which of the following is NOT a possible probability?

a. 25/100

b. -1.25

c. 1

Â Â Â Â Â Â Â Â Â  d. 0

10. Which one of these variables is a continuous random variable?

Â The time it take a randomly selected student to complete an examÂ TheÂ  number of tattoos a randomly selected person hasÂ The number of women taller than 68 inches in a random sample of 5Â Â Â Â  women.Â TheÂ numberÂ ofÂ correctÂ guessesÂ anÂ aÂ multipleÂ choiceÂ test.

SelectionÂ ofÂ favoriteÂ fruitsÂ andÂ responsesÂ ofÂ orange,Â grape,Â apple,Â kiwiÂ orÂ otherÂ manyÂ wereÂ recordedÂ are

Probability distributionBinomial distributionPoisson distributionÂ None

If theÂ  z â€“ score of normal distribution is 2.5, the mean of the distribution is 45 and the standard deviation of normal distribution is 3 then the value of X for a normal distribution is:Â

97.5Â Â Â Â Â Â 47.5Â Â Â Â Â Â 52.567.5

The grades on a math midterm are normally distributed with Î¼Â  and

0.432.32âˆ’0.36â€“Â 0.43

Express the confidence interval -0.001< p < 0.559 in the form .

0.279 - 0.28Â Â Â populationÂ population parameter

Â Â Â Â Â Â Â Â  c.Â Â  confidence coefficient

Â Â Â Â Â Â Â Â  d.Â Â  sample size

Part-II (Multiple Choice Questions)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (15 marks, 1 Mark Each)

 Q. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A.

Section â€“III

Answer the following Short Type QuestionsÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (12 marks, 2 Mark Each)

Construct a stem-and Leaf of the following dataConstruct histogram of the following frequency tableLet the sample space . Find the followingP (Ä€)Â A test consists of 10 multiple-choice questions with five choices for each question. As an experiment, you GUESS on each answer without even reading the questions. What is the probability of getting exactly 6 questions correct on this test? Also find mean and variance of binomial distribution.Z follows a standard normal distribution. Find

Â Â Â Â Â Â Â  a) P(Z < 2.37)

Â Â Â Â Â Â Â  b)Â  P(Z > 1.82)

Â Â Â Â Â Â Â  c)Â Â  P(-1.18 < Z < 2.1)

Flipkart online company interested in knowing the percentage of adult who buy clothing on line. How many adult must be surveyed in order to be 95% confidence that the sample percentage is in error by no more than 3 percentage point and 66% of adult by clothing on line.ConstructÂ  a grouped frequency table Â for the following set of time in second (Put them in 6 equal length classes). And also calculate relative frequency, relative cumulative frequency.

83

31

40

88

89

80

62

35

60

75

30

30

85

85

72

35

50

42

83

75

63

85

46

60

30

65

79

59

30

70

K=

Minimum =

Maximum =

Range=Â Â Â  ,Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Length of classes=

The marks of 5 students in a statistics test that had a maximum possible mark of 100 are given below:
72 76 73 76 78

Find the mean, mode, median, standard deviation and variance of this set of data values.

Consider the following distribution of gender and major of students in an introductory statistics class:
 Social Science Science Total Female 20 10 30 Male 20 10 30 Total 40 20 60

a. Find the probability that a randomly selected student is from social science.

b. Find the probability that a randomly selected student is from social science major given that they are female.

c. Find the probability that a randomly selected student is a Male student.

DuringÂ theÂ summerÂ months,Â aÂ rentalÂ agencyÂ keepsÂ trackÂ ofÂ theÂ numberÂ ofÂ chainÂ sawsÂ itÂ rentsÂ eachÂ dayÂ duringÂ aÂ givenÂ periodÂ andÂ XÂ denotesÂ theÂ numberÂ ofÂ sawsÂ rentedÂ perÂ day.Â DescribeÂ aÂ probabilityÂ distribution,Â ifÂ itÂ isÂ probabilityÂ distribution,Â findÂ theÂ mean,Â variance,Â andÂ standardÂ deviationÂ forÂ theÂ probabilityÂ distribution.Listed below are speeds (mi/h) measured from 12 ransom sample at 3.30 pm on a weekday in traffic. The speed limit for this road is 65mi/h. Use the sample data to construct 95% confidence interval for the mean speed.

Â Â Â  62, 61, 61, 57,61, 54, 59, 58, 59, 69, 60, 67

Assignment NO. 1 week2-week7
Student Full Name:___________________________________ .
Student ID:__________________________________________ .
CRN No:____________________________________________ .
Branch: _____________________________________________. Total Points STATISTICS
____/15
(STAT-101)
MCQ
____/15
True/False Short Answer ____/12 Long Answer ____/18 Total ____/60 Day: Monday
Date: 23.5.1438 Good Luck STATISTICS (STAT-101)
Marks- 60
Answer all the Questions on the same question paper. Section-I
State whether the following statements are True or False. (15 marks, 1 Mark Each)
1. The amount of milk that a cow produces in a gallon an example of
continuous data.
2. Systematic Sampling is sampling in which data is obtained by selecting
every kth object.
3. Any characteristic of a population distribution may properly be referred to
as a parameter
4. Populations are always infinite.
5. The population mean and the population median will not generally be
equal to one another.
6. There are four quartiles that divided the data into four equal parts.
7. The probability of an impossible event is one.
8. If A and B are disjoint events, then in conditional probability
P (A|B) = P (A).
9. Mean value over an infinite number of observations of the variables is the
expected value of random variables.
10. Poisson distribution is a continuous probability distribution.
11. In the standard normal distribution the standard deviation is always
exactly zero.
12. The distribution of sample Â´x will as the sample size increases, approach a normal distribution.
13.A point estimate is a single value or point used to approximate a
population parameter.
14.A critical value is a Z-score separating unlikely value from those that are
likely to occur.
15. As the sample size increases, the sampling error will increase as well.
Section-II
(Multiple Choice Questions) (15 marks, 1 Mark Each) 1. The subject in which college students major.
a. Ordinal
b. Nominal
c. Ratio
d. Interval
Page 2 of 9 2. Which one of the following variables is not categorical?
a. The choice on a test item: true or false.
b. The gender of a person: male or female
c. The age in years of a person.
d. The marital status of a person: single, married, divorced, other.
3. A distribution of data that is the left half of its histogram is roughly a
mirror image of its right half called:
a. Skewed
b. Symmetric
c. both a and b
d. None
4. A sample value that lies very far away from the majority of the other
sample values is
a. The center.
b. A distribution.
c. An outlier.
d. a variance.
5. Which of the following are examples of a variable?
a. Gender of a high school graduate.
b. Number of major credit cards a person has.
c. Type of automobile transmission.
d. All of the above. 6. Which of the following is not a measure of variability?
a. Variance.
b. Standard deviation.
c. Mean.
d. Median.
7. An urn contains 6 blue or white balls, 4 of them are blue, what is the
Page 3 of 9 probability of getting white ball?
a. 0.7
b. 1/3
c. 3
d. 1
8. What is the probability of rolling a die and getting either a 1 or a 6? a. 1/3 b. 1/2 c. 6/21 d. 8/2 9. Which of the following is NOT a possible probability?
a. 25/100
b. -1.25
c. 1
d. 0
10. Which one of these variables is a continuous random variable?
a. The time it take a randomly selected student to complete an exam
b. The number of tattoos a randomly selected person has
c. The number of women taller than 68 inches in a random sample of 5
women.
d. The number of correct guesses an a multiple choice test. 11.Selection of favorite fruits and responses of orange, grape, apple, kiwi or
other many were recorded are
a.
b.
c.
d. Probability distribution
Binomial distribution
Poisson distribution
None 12.If the z â€“ score of normal distribution is 2.5, the mean of the distribution
is 45 and the standard deviation of normal distribution is 3 then the value
of X for a normal distribution is:
a. 97.5
b. 47.5
Page 4 of 9 c. 52.5
d. 67.5
13.The grades on a math midterm are normally distributed with Î¼=68 and
Ïƒ = 5.5. If a student scored 66 on the exam, the z-score of his exam grade
rounded to two decimal places is
a. 0.43
b. 2.32
c. âˆ’0.36
d. â€“ 0.43
14.Express the confidence interval -0.001&lt; p &lt; 0.559 in the form ^p Â± E .
a. 0.279 - 0.28
b. 0.279 Â±0.5
c. 0.279 Â±0.28 d. 0.28 Â± 0.5
15. A confidence interval is a range of values used to estimate the true value
of a
a. population
b. population parameter
c. confidence coefficient
d. sample size Part-II (Multiple Choice Questions)
Q. 1
2
3
4
5
6
7
8
A. 9 (15 marks, 1 Mark Each)
10 11 12 13 14 15 Section â€“III
(12 marks, 2 Mark Each) Answer the following Short Type Questions
1. Construct a stem-and Leaf of the following data 84 49 61 40 83 67 45 66 70 69 80 58 68 60 67 72 73 70 57 63 70 78 52 67 Page 5 of 9 53 67 75 61 70 81 76 79 75 76 58 31 2. Construct histogram of the following frequency table 3. Let the sample space {a, b , c , d , e , f , j }, A={a,b,c}, and B={b,e} following
a) b) P (A ) P (A U B ) Page 6 of 9 . Find the c) P (B / A ) d) P (Ä€)
4. A test consists of 10 multiple-choice questions with five choices for each
question. As an experiment, you GUESS on each answer without even
reading the questions.
What is the probability of getting exactly 6 questions correct on this test?
Also find mean and variance of binomial distribution.
5. Z follows a standard normal distribution. Find
a) P(Z &lt; 2.37)
b) P(Z &gt; 1.82)
c) P(-1.18 &lt; Z &lt; 2.1)
6. Flipkart online company interested in knowing the percentage of adult
who buy clothing on line. How many adult must be surveyed in order to
be 95% confidence that the sample percentage is in error by no more than
3 percentage point and 66% of adult by clothing on line. Section â€“IV
(18 marks, 3 Mark Each) Answer the following Long Type Questions 1. Construct a grouped frequency table for the following set of time in
second (Put them in 6 equal length classes). And also calculate relative
frequency, relative cumulative frequency.
83
31
40
88
89
80 62 35 60 75 30 30 85 85 72 35 50 42 83 75 63 85 46 60 30 65 79 59 30 70 K=
Minimum =
Maximum =
Range= , Length of classes=
Page 7 of 9 2. The marks of 5 students in a statistics test that had a maximum possible
mark of 100 are given below:
72 76 73 76
78
Find the mean, mode, median, standard deviation and variance of this set of
data values.
3. Consider the following distribution of gender and major of students in an
introductory statistics class:
Female
Male
Total Social Science
20
20
40 Science
10
10
20 Total
30
30
60 a. Find the probability that a randomly selected student is from social
science.
b. Find the probability that a randomly selected student is from social
science major given that they are female.
c. Find the probability that a randomly selected student is a Male student.
4. During the summer months, a rental agency keeps
track of the number of chain saws it rents each day
during a given period and X denotes the number of
saws rented per day. Describe a probability
distribution, if it is probability distribution, find the
mean, variance, and standard deviation for the
probability distribution.
x
P(x) 0
0.5 1
0.33 2
0.17 5. Suppose a student measuring the boiling temperature of a certain liquid
observes the readings (in degrees Celsius) 102.5, 101.7, 103.1, 100.9,
100.5, and 102.2 on 6 different samples of the liquid. He calculates the
sample mean to be 101.82. If he knows that the standard deviation for this
procedure is 1.2 degrees, what is the confidence interval for the population
mean at a 95% confidence level? Page 8 of 9 6. Listed below are speeds (mi/h) measured from 12 ransom sample at 3.30
pm on a weekday in traffic. The speed limit for this road is 65mi/h. Use
the sample data to construct 95% confidence interval for the mean speed.
62, 61, 61, 57,61, 54, 59, 58, 59, 69, 60, 67 Good luck Page 9 of 9

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