MIDTERM EXAMINATION
Fall 2010
STA301 - Statistics and Probability
Time: 60 min
Marks: 40
Important Note:
Final Term 2010 Paper. Selected answers are not right/wrong but they are attempted by the candidate these answers could be right or wrong.
Exam Date: | Thu, |
Question No: 1 ( Marks: 1 ) - Please choose one
The standard deviation of -1, -1, -1, -1 will be
► 1
Selected answer -1
► 0
► Does not exist
Question No: 2 ( Marks: 1 ) - Please choose one
10! =………….
► 362880
Selected answer 3628800
► 362280
► 362800
Question No: 3 ( Marks: 1 ) - Please choose one
Evaluate: (9-4)!
► 362880
Selected answer 120
► 24
► 6
Question No: 4 ( Marks: 1 ) - Please choose one
When two coins are tossed simultaneously, P(1 Heads) is equal to_________:
► 1
► 1/2
► 1/4
Selected answer 3/4
Question No: 5 ( Marks: 1 ) - Please choose one
How many percent of values are less than 4th decile in a symmetric distribution:
► 4
► 40
► 14
Selected answer 24
Question No: 6 ( Marks: 1 ) - Please choose one
First moment about origin is always equals to:
► Mean
Selected answer Variance
► Standard Deviation
► Zero
Question No: 7 ( Marks: 1 ) - Please choose one
If we plot the paired observation
Selected answer Frequency polygon
► Frequency histogram
► Scatter diagram
► Cumulative frequency polygon
Question No: 8 ( Marks: 1 ) - Please choose one
Symbolically, a marginal probability is:
► P(AB)
► P(A)
► P(A/B)
Selected answer P(AUB)
Question No: 9 ( Marks: 1 ) - Please choose one
Stem and leaf was introduced by:
Selected answer Francis Galton
► Friedman
► John Tukey
► Pearson
Question No: 10 ( Marks: 1 ) - Please choose one
According to empirical rule approximately 95% of the measurements will fall under which interval?
►
Selected answer
►
►
Question No: 11 ( Marks: 1 ) - Please choose one
What is ‘ ’ in the formula of mode:
► First frequency
► Last frequency
Selected answer Maximum frequency
► Minimum frequency
Question No: 12 ( Marks: 1 ) - Please choose one
The branch of Statistics that is concerned with the procedures and methodology for obtaining valid conclusions is called:
► Descriptive Statistics
Selected answer Advance Statistics
► Inferential Statistics
► Sampled Statistics
Question No: 13 ( Marks: 1 ) - Please choose one
Data arranged in ascending or descending order is called:
► Grouped data
► Arrayed data
► Ungrouped data
Selected answer Raw data
Question No: 14 ( Marks: 1 ) - Please choose one
Which one is commonly called a bell shaped distribution?
► Symmetrical
► Bimodal
Selected answer Skewed
► U shaped
Question No: 15 ( Marks: 1 ) - Please choose one
Which one of the following is a suitable frequency distribution for an ogive:
► A relative frequency distribution
► A frequency distribution
Selected answer A joint frequency distribution
► A cumulative frequency distribution
Question No: 16 ( Marks: 1 ) - Please choose one
Which one of the following is not a type of frequency curve?
► The symmetrical frequency curve
Selected answer The extremely skewed frequency curve
► The U-shaped frequency curve
► Frequency polygon
Question No: 17 ( Marks: 1 ) - Please choose one
For the given set of observations 1, 4, 4, 4 and 7, which statement is true:
►
Selected answer
►
►
Question No: 18 ( Marks: 1 ) - Please choose one
If the probability of one event does not affected by the occurrence of another event then both events are:
► Dependent
► Not Mutually Exclusive
► Mutually Exclusive
Selected answer Independent
Question No: 19 ( Marks: 1 ) - Please choose one
Two events A and B are statistically independent when:
►
►
Selected answer
►
Question No: 20 ( Marks: 1 ) - Please choose one
Which one of the following is equal to “explained variation divided by total variation”?
► Sum of squares due to regression
► Coefficient of determination
► Standard error of estimate
Selected answer Coefficient of correlation
Question No: 21 ( Marks: 2 )
For a certain data,
Find moment ratio
Answer
solution:
the moment ration can be found by the following way.
0 + 2.64 + 5.6 + 28.30 = 36.54/4 = 9.14
Question No: 22 ( Marks: 2 )
Indicate whether the following statement is true or false. If false, indicate why.
If P (A/B) = 0, then A and B are mutually exclusive.
Answer
Solution:
The statement is false because
If P(A/B) than there is a probability of 1/2 for each value.
for example if we toss a coin then the head and the tail both will have the same chance of showing of so it shows that,
P(A/B) = 1/2
Question No: 23 ( Marks: 3 )
If mean of a distribution is 10 and standard deviation is 2.5. Find out the limits by applying Chebychev’s Inequality for k= 3. How much fraction of data will lie between these two limits?
Answer
Solution:
Limit 0 = (S.d/Mean) * k
= (2.5/10)*3 = 0.75
Limit m = 10/(2.5*3) = 1.33
Question No: 24 ( Marks: 3 )
Two events A and B are such that P(A)=1/4, P(A/B)=1/2 and P(B/A)=2/3
Are A and B mutually exclusive events?
Answer
Solution:
Both A and B are mutually exlusive because of the following fact.
If we say that the header of a coin is A and the tail of the coin is B than
If we toss at the same time than the probability of a header of coin will be as
p(A) = 1/4
And
If we toss the two coins at the same time than the probibility of a header of one coin will be as
P(A/B) = 1/2
and the probibility of the tail of the two coins will be
B/A) = 2/3
Question No: 25 ( Marks: 5 )
Find the probability distribution of number of boys in families having three children, assuming equal probabilities for boys and girls.
Answer
Blank Data
Question No: 26 ( Marks: 5 )
For the given equation Y = a + b X, explain the four terms a, b, X and Y.
Answer
By ADEEL ABBAS, Bhakkar. AdeelAbbasbk@gmail.com
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