Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

The overall percentage of passes in a certain examination is $80$.If $6$ candidates appear in the examination what is the probability that atleast $5$ pass the examination.

Can you answer this question?

1 Answer

0 votes
  • A random variable $X$ is said to follow a binomial distribution of its probability mass function is given by
  • $P(X=x)=p(x)=\left\{\begin{array}{1 1}nC_xp^xq^{n-x},&x=0,1.......n\\0,&otherwise\end{array}\right.$
  • Constants of Binomial Distribution :
  • Mean = np
  • Variance = npq
  • Standard deviation =$\sqrt{ variance }=\sqrt{ npq}$
  • In a bionomial distribution Mean > Variance.
  • The parameters of the distribution are $n,p\quad X\sim B(n,p)$
Step 1:
Let $X$ be the random variable denoting the number of students that pass in an exam out of a total of 6 students.
Probability that a student will pass =$\large\frac{80}{100}=$$0.8=p$
$X\sim B(6,0.8)$ and $q=1-0.8=0.2$
Step 2:
The probability distribution $X$ is given by
$P(X=x)=6C_x(0.8)^x(0.2)^{6-x}\qquad x=0,1,2......6$
Step 3:
Probability that at least 5 pass in the exam =$P(X\geq 5)=P(X=5)+P(X=6)$
$\qquad\qquad\qquad\qquad\qquad\qquad\qquad=(0.8)^5\times 2$
answered Sep 18, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App