Quantitative Aptitude - Theoretical Distributions
Exam Duration: 45 Mins Total Questions : 30
A theoretical probability distribution
- (a)
Does not exist
- (b)
Exists only in theory.
- (c)
Exists in real life
- (d)
Both (b) and (c)
In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(x=12) is
- (a)
1/6
- (b)
0
- (c)
1/7
- (d)
None
In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(x < 15) is
- (a)
2/3
- (b)
1/3
- (c)
1
- (d)
None
When the no. of trials is large then
- (a)
Normal
- (b)
Poisson
- (c)
Binomial
- (d)
None distribution is used
In a Poisson distribution,
- (a)
Mean and standard deviation are equal
- (b)
Mean and variance are equal.
- (c)
Standard deviation and variance are equal
- (d)
Both (a) and (b)
In Poisson distribution, probability of success is very close to
- (a)
1
- (b)
-1
- (c)
0
- (d)
None
Poisson distribution may be
- (a)
Always symmetric
- (b)
Always positively skewed
- (c)
Always negatively skewed
- (d)
Symmetric only when m = 2
No. of radio-active atoms decaying in a given interval of time is an example of
- (a)
Binomial distribution
- (b)
Normal distribution
- (c)
Poisson distribution
- (d)
None
If for a Poissonvariable X, f(2) = 3 f(4), what is the variance of X?
- (a)
2
- (b)
4
- (c)
√2
- (d)
3
A random variable x follows Poisson distribution and its coefficient of variation is 50. What is the value of P(x>1/x>0)?
- (a)
0.1876
- (b)
0.2341
- (c)
0.9254
- (d)
0.8756
The manufacturer of a certain electronic component is certain that two per cent of his product is defective. He sells the components in boxes of 120 and guarantees that not more than two per cent in any box will be defective. Find the probability that a box, selected-at random, would fail to meet the guarantee? Given that e-2.40 = 0.0907
- (a)
0.26
- (b)
0.52
- (c)
0.43
- (d)
0.86
A car hire firm has 2 cars which is hired out everyday. The number of demands per day for a car follows Poisson distribution with mean 1.20. What is the proportion of days on which some demand is refused? (Given e1.20= 3.32)
- (a)
0.25
- (b)
0.3012
- (c)
0.2235
- (d)
0.3450
For a binomial distribution, there may be
- (a)
One mode
- (b)
Two modes
- (c)
(a) or (b)
- (d)
Many mode
The maximum value of the variance of a binomial distribution with parameters n & p is
- (a)
n/2
- (b)
n/4
- (c)
np(1-p)
- (d)
2n
If in Binomial distribution np=9 and npq=2.25 then p and n are equal to is equal to
- (a)
0.25,36
- (b)
0.75,12
- (c)
1, 9
- (d)
None
What is the no. of trials of a binomial distribution having mean and SD as 3 and 1.5 respectively?
- (a)
2
- (b)
4
- (c)
8
- (d)
12
A random variable x follows Binomial distribution with mean 2 and variance 1.6. then the value of p is
- (a)
1/5
- (b)
4/5
- (c)
3/5
- (d)
None
Out of 128 families with 4 children each, how many are expected to have atleast one boy and one girl?
- (a)
100
- (b)
105
- (c)
108
- (d)
112
A die is thrown 100 times. If getting an even number is considered a success, then the variance of the number of successes is
- (a)
50
- (b)
25
- (c)
10
- (d)
100
If 15 dates are selected at random, what is the probability of getting two Sundays
- (a)
0.36
- (b)
0.44
- (c)
0.29
- (d)
0.57
If x is a binomial variate with parameter 15 and 1/3, what is the value of mode of the distribution?
- (a)
5 and 6
- (b)
5
- (c)
5.50
- (d)
6
For continuous variates ________ distribution is used.
- (a)
Normal
- (b)
Poisson
- (c)
Binomial
- (d)
None
The normal curve is
- (a)
Bell-shaped
- (b)
U-shaped
- (c)
J-shaped
- (d)
Inverted J-shaped
The curve of _____ distribution is unimodal and bell-shaped with the highest point over the mean
- (a)
Poisson
- (b)
Normal
- (c)
Binomial
- (d)
None
The interval (μ - 3σ, μ + 3σ ) covers
- (a)
95% area of a normal distribution
- (b)
96% area of a normal distribution
- (c)
99% area of a normal distribution
- (d)
All but 0.27% area of a normal distribution
A random variable X has probability density function given by\( f(x) =\begin{cases}Ax^2 (1- x),o < x < 1 \\ O,otherwis \end{cases}\) then the value of A is
- (a)
2
- (b)
3
- (c)
1/12
- (d)
12
The mean of a normal distribution is 500 and 16 per cent of the values are greater than 600. What is the standard deviation of the distribution?
- (a)
75
- (b)
100
- (c)
50
- (d)
60
_______ distribution has a greater spread than Normal distribution curve
- (a)
T
- (b)
Binomial
- (c)
Poisson
- (d)
None
For an unknown parameter, how many interval estimate exists
- (a)
One
- (b)
Two
- (c)
Many
- (d)
Some
t-test can be used only when the sample has been taken from _______ population
- (a)
Binomial
- (b)
Poisson
- (c)
Normal
- (d)
Exponential