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Maths MCQ

Binomial Distribution · Maharashtra Board STD 12 Science (MSBSHSE - English Medium). 5 questions.

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MCQ 12 Marks
If the mean and variance of a binomial distribution are 5 and 2.5 respectively, then $n=$
  • A
    5
  • B
    10
  • C
    18
  • D
    15
Answer

Given: Mean = np = 5 ....(1)
           Variance = npq = 2.5 ....(2)
Dividing (2) by (1): $\frac{n p q}{n p}=\frac{2.5}{5} \therefore q=\frac{1}{2}$
$\therefore p=1-q=1-\frac{1}{2}=\frac{1}{2}$
From (1): np = 5,
$\therefore n\left(\frac{1}{2}\right)=5, \therefore n=10$

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MCQ 22 Marks
If $X \sim B(n, P)$ and $E(X)=12, \operatorname{Var}(X)=4$, then the value of $n$ is $\ldots . .$.
  • A
    3
  • B
    48
  • C
    18
  • D
    36
Answer
coming soon
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MCQ 32 Marks
The expected value of the number of heads obtained when three fair coins are tossed simultaneously is ....
  • A
    1
  • B
    1.5
  • C
    0
  • D
Answer

(B) 1.5
p=1/2
q=1/2    [∵q=1-(p)]
n=3
Expected value E(X) = np =$3 \times \frac{1}{2}=1.5$

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MCQ 42 Marks
Given that $X \sim B (n=10, p)$. If $E ( X )=8$, then the value of $p$ is...
  • A
    0.6
  • B
    0.7
  • C
    0.8
  • D
    0.4
Answer

(c)
Since X ~ B(n = 10, p),
E(x) = np
10p = 8
p = 0.8

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MCQ 52 Marks
Given $X \sim B (n, p)$. If $p=0.6$ and $E ( X )=6$, then the value of Var. $( X )$ is......
  • A
    2.4
  • B
    2.6
  • C
    2.5
  • D
    2.3
Answer
coming soon
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MCQ - Maths STD 12 Science Questions - Vidyadip