Probability

Given below are two statements about a normally distributed data.
Statement I : 95.45% of the occurrences will lie between .
Statement II : 68.27% of the occurrences will lie between .
In the light of the above statements, choose the correct answer from the options given below:

Read the given statements about correlation carefully and identify the correct statements.
A. A positive relation means that the variables vary in the same direction.
B. If two or more variables are related in a statistical way, is sufficient to conclude that a cause and effect relation exists.
C. A negative relation means that the two variables vary in the opposite direction.
D. Pearson's Product-Moment Method is a method used to calculate r.
Choose the correct answer from the options given below:

Match List I with List II :

List I (Method)		List II (Characteristic)
(A)	Mean	(I)	Identify what is most common
(B)	Median	(II)	Based on sound mathematics
(C)	Mode	(III)	Square-root of the variance
(D)	Standard deviation	(IV)	Divides into 2 equal parts

Choose the correct answer from the options given below:

If 2u=5x, is the relation between two variables u and x, and harmonic means of x is 0.8, find the harmonic mean of u.

The variance of a series of numbers 2, 3, 11 and x is 12.25. Find the value of x.

Which of the following assertions are correct?
(A) Adding 7 to each entry in a list adds 7 to the mean of the list.
(B) Adding 7 to each entry in a list adds 7 to the standard deviation of the list.
(C) Doubling each entry in a list doubles the mean of the list.
(D) Doubling each entry in a list leaves the standard deviation of the list unchanged.
Choose the most appropriate answer from the options given below :

If the mean of 18, 19, x, 25 and 26 is 21, then find the mean of 5, 11, 13, 19 and (3x-1)

A bag contains 10 red beads (R)and 5 black beads (B). A bead is taken out of the bag at random, its color is noted and then it is not placed back in the bag. Calculate the probability that first two beads are red.

The mean deviation from the mean of the AP: a,a+d, a+2d,..., a+2nd, is

The mean deviation from the mean of the AP a, a+d, a+2d,..... a + 2nd is

Match List-I and List-II

LIST I		LIST II
A.	Addition Theorem on probability	I.
B.	Binomial distribution	II.
C.	Baye's rule	III.
D.	Multiplication theorem on prob	IV.

Choose the correct answer from the options given below:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: An elevator starts with m passengers and stops at n floors (m n). The probability that no two passengers alight at the same floor is
Reason R: If (n + 1) p is an integer, say m, then is maximum when r = m or r = m -1
In the light of the above statements, choose the most appropriate answer from the options given below :

A person goes in for an examination in which there are four papers with a maximum of m marks from each paper. The number of ways in which one can get 2m marks is

If each of n numbers x_i = i is replaced by (i + 1)x_i, then the new mean is

If each observation of a Row data whose variance is \sigma ² is multiplied by h, then the variance of the new set is

Which statistical method is best suitable for testing the goodness of fit between an observed and expected distribution?

A unit analysis that takes on different values is known as

A statement or a tentative proposition of potential relationship between two or more variables is known as

Which of the following is an example of non-probability sampling?

The term used to describe the most frequently occurring category of a non-numeric variable

A hypothesis which shows no relationship or no significant difference between groups on a variable.

Calculate the mean of the following numbers: 100, 200, 600

An untested statement about the relationship between concepts within a given theory is called

The middle value in a series of numbers, the point that neither exceeds nor is exceeded by more than 50 percent of the total observation ?

A bag contains 1 red, 3 green, 2 blue and 4 yellow balls. If a single ball is chosen at random from the bag, then what is the probability that it is yellow or green?

Calculate the value of median from the given data:
2.90, 3.57, 3.73, 2.98, 3.64, 3.75
3.30, 3.62, 3.76, 3.38, 3.66, 3.76

If x is continuous random variable. and a probability density function The value of k is

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion (A): The numeric differences in the forecast of demand and actual demand is known as forecast error (e).
Reasons (R): Mean Absolute Deviation .
In the light of the above statements, choose the most appropriate answer from the options given below:

A single 6-sided dice is rolled, then the probability of getting an odd number is

Two fair dice are thrown. The probability that the number of times the dice exceeds 3 and that the second exceeds 4 will be

A committee of two persons is selected from two men and two women. What is the probability that the committee will have at least one man?

Ten cards numbered 1 to 10 are placed in a box and one card is drawn randomly. If it is known that the number on drawn card is more than 2. The probability that it is an odd number is: