Page 177 - Engineering Mathematics Workbook_Final

Probability & Statistics

is from x = − to x = +. The CDF 83. What is the probability that at most 5
for this function for x  0 is defective fuses will be found in a box
of 200 fuses, if 2% of such fuses are
a defective?
bx
(a) e
b (a) 0.82 (b) 0.79

a (c) 0.59 (d) 0.82
−
(b) (2 e − bx )
b [ESE-2017-EE]

a 84. If X is a normal variate with mean 30
bx
(c) − be
b and standard deviation 5, what is
Probability (26  X  34 ) , given
a
−
+
(d) ( 2 e − bx ) [ESE-2017-EC] ( A z = 0.8 = ) 0.2881 where A
b
represents area.
81. A random variable X has the density (a) 0.2881 (b) 0.5762

1
function ( ) x = K , where (c) 0.8181 (d) 0.1616
f
+
1 x 2
− x  . Then the value of K is [ESE-2017-EE]

1 85. In a sample of 100 students, the mean
(a)  (b) of the marks (only integers) obtained
 by them in a test is 14 with its

standard deviation of 2.5 (marks
1
(c) 2 (d) obtained can be fitted with a normal
2 distribution). The percentage of

students scoring 16 marks is
[ESE-2017-EE]
(a) 36 (b) 23
82. A random variable X has a
probability density function (c) 12 (d) 10
 kx e x ; x  0
n −

f ( ) x =  (n is (Area under standard normal curve
 0; otherwise between z = 0 and z = 0.6 is 0.2257;

an integer) with mean 3. The value of and between z = 0 and z = 1.0 is
{k, n} are 0.3413) [ESE-2018-EE]

  1     1  
(a)  ,1 (b)  ,2 86. Consider a random variable to which
  2     4   a Poisson distribution is best fitted. It

  1   happens that P = 2 P on this
(c)  ,2 (d) {1, 2} (x= ) 1 3 (x= ) 2
  2   distribution plot. The variance of this

[ESE-2017-EE] distribution will be

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