The mean and standard deviation of a binomial distribution are 12 and 2 respectively. What is the number of trails?

This question was previously asked in
NDA (Held On: 23 April 2017) Maths Previous Year paper
View all NDA Papers >
  1. 2
  2. 12
  3. 18
  4. 24

Answer (Detailed Solution Below)

Option 3 : 18
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
5.8 K Users
150 Questions 600 Marks 150 Mins

Detailed Solution

Download Solution PDF

Concept:

  • Mean = μ = np
  • \({\rm{Standard\;deviation}} = {\rm{\sigma }} = \sqrt {{\rm{npq}}} {\rm{\;}}\)


Where n = number of trials; p = probability of success; q = (1-p) = probability of failure

Calculation:

Given: Mean = μ = np = 12

\({\rm{Standard\;deviation}} = {\rm{\sigma }} = \sqrt {{\rm{npq}}} = 2\)

∴ Variance = σ2 = npq = 4

⇒ 4 = np (1−p) = 12(1−p) 

 ⇒ 4/12 = (1−p) 

⇒ (1 – p) = 1/3

⇒ p = 1 – 1/3

∴ p = 2/3

Again; μ = np = 12

∴ n = 12/p = 12 × (3/2) = 18

Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

More Probability Questions

Get Free Access Now
Hot Links: teen patti wealth teen patti 3a teen patti - 3patti cards game teen patti rules