Question
Download Solution PDFThe mean and standard deviation of a binomial distribution are 12 and 2 respectively. What is the number of trails?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- 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
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