Probability and Statistics - Engineering Mathematics - Mining Engineering Previous Year Questions

1

2007 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2007

The measures of dispersion are

A

range, variance, and standard deviation

B

mean, median, and variance

C

mean, mode, and skewness

D

mean, range, and variance

Open complete paper

2

2007 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2007

In a single server queueing model with constant arrival rate, which one of the following probability distributions is followed by the inter-arrival times of the customers at the service facility?

A

binomial

B

Poisson

C

Weibull

D

exponential

Open complete paper

3

2007 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2007

Consider the following data for the grade of iron ore from a working bench over past 5 weeks Week 1 2 3 4 5 Grade (% Fe) 62.1 61.0 60.5 62.5 62.0 The 3-week moving average forecast for the grade, in % Fe, in the 6th week is

A

61.66

B

61.90

C

62.20

D

62.50

Open complete paper

4

2007 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2007

The random variable X has the following probability mass function P(4) = 1/4, P(8) = 1/4, P(12) = 1/4, P(16) = 1/4. The expected value of X is

A

1

B

3

C

10

D

12

Open complete paper

5

2007 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2007

The unbiased estimate of variances of alumina and silica in (%)² respectively are

A

2.5, 2.5

B

2.0, 2.5

C

2.5, 2.0

D

2.0, 2.0

Open complete paper

6

2008 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2008

Q.2 If X is a continuous random variable and f(x) defines its probability density function, then the expected value of X is

A

\(\int_{-\infty}^{\infty} f(x) dx \)

B

\(\sum_{i=-\infty}^{\infty} x_i \)

C

\(\sum_{i=-\infty}^{\infty} x_i f(x_i) \)

D

\(\int_{-\infty}^{\infty} x f(x) dx \)

Open complete paper

7

2008 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2008

Daily production measured for a period of 50 days in a coal mine exhibits normal distribution with mean 1200 tpd and standard deviation 100 tpd. The 95% confidence interval of daily production (standard normal variable Z at 0.025 level of significance is 1.96) in tpd is

A

1200 ± 120.5

B

1200 ± 96.0

C

1200 ± 39.6

D

1200 ± 27.7

Open complete paper

8

2008 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2008

In an iron ore deposit alumina is distributed with μ = 3 % and σ = 0.5%; whereas silica is distributed with μ = 2.5 % and σ = 0.8%. The combined alumina and silica (as impurities) has μ and σ, in percentage respectively as

A

(5.5, 0.94)

B

(5.5, 1.3)

C

(0.5, 0.3)

D

(5.5, 0.62)

Open complete paper

9

2009 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2009

In a normal (Gaussian) distribution curve, the area between one standard deviation from mean on either side in percent is

A

50

B

68

C

86

D

95

Open complete paper

10

2009 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2009

A measure of dispersion of a sample data set is

A

mean

B

median

C

mode

D

standard deviation

Open complete paper

11

2009 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2009

The mean of the cubes of the first \( n \) natural numbers is

A

\(\frac{n(n+1)^2}{4} \)

B

\(\frac{n(n+1)(n+2)}{8} \)

C

\(\frac{n^2+1}{n} \)

D

\(\frac{n^3}{4} \)

Open complete paper

12

2009 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2009

The following data represent the number of workers suffering from pneumoconiosis in 10 coal mines.

Mine	I	II	III	IV	V	VI	VII	VIII	IX	X
Number	10	16	14	15	14	12	17	13	15	12

The number of mines falling above the 50^th percentile in terms of the number of workers suffering from pneumoconiosis is

A

2

B

3

C

4

D

5

Open complete paper

13

2009 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2009

Probability that there is a queue (more than one workman) at the service counter is

A

0.24

B

0.36

C

0.40

D

0.60

Open complete paper

14

2010 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2010

The mean and the standard deviation of the grade of iron ore in a deposit are 62% and 5% respectively. The coefficient of variation of the grade in % is

A

24.8

B

12.4

C

8.0

D

4.0

Open complete paper

15

2010 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2010

The variance of failure time (time to failures) of an electric motor in shovel is 1600 hr². If the failure time follows an exponential distribution, the expected failure time in hr is

A

40

B

80

C

800

D

1600

Open complete paper

16

2010 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2010

Pull from an underground tunnel blasting is normally distributed with a mean of 100 tonnes and variance 100 (tonnes)². The probability that the tonnage value from a blast exceeds 110 is

A

0.60

B

0.80

C

0.16

D

0.32

Open complete paper

17

2010 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2010

The probabilities of hitting a target by A and B are 1/3 and 2/5 respectively. A shoots at the target once, followed by B shooting at the target once. The probability of hitting the target is

A

2/15

B

5/15

C

8/15

D

9/15

Open complete paper

18

2010 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2010

Which of the following options is the closest in meaning to the word below: Exhort

A

urge

B

condemn

C

restrain

D

scold

Open complete paper

19

2010 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2010

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair. Preamble : Constitution

A

amendment : law

B

prologue : play

C

episode : serial

D

plot : story

Open complete paper

20

2010 · Mining Engineering · Engineering Mathematics · Probability and Statistics

Mining Engineering (MN) 2010

Choose the most appropriate word from the options given below to complete the following sentence: The committee wrote a ______ report, extolling only the strengths of the proposal.

A

reasonable

B

supportive

C

biased

D

fragmented

Open complete paper