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The 95% confidence level limits to a population mean are 94.12 - 105.88. Find population standard deviation if sample size is 100.
1. 15
2. 30
3. 45
4. 60

1 Answer

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Best answer
Correct Answer - Option 2 : 30

Given

Confidence level limits = 94.12 - 105.88

Sample size = 100

Concept 

± 1.96 SE

SE = 1.96 σ/√n

Calculation

SE = 1.96 σ/√100

⇒ SE = (1.96 × σ)/10

⇒ SE = 0.196 σ 

⇒ p + 1.96 σ = 105.88

⇒ 100 + 0.196σ = 105.88

⇒ 0.196 = 5.88

⇒ σ = 5.88/0.196

∴ The standard deviation is 30

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