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A random sample of 100 ball bearings selecte from a shipment of 2000 ball bearing has an average diameter of 0.354 inches with standard deviation 0.048 inches. The 95% confidence interval for the average diameter of these 2000 ball bearings is:
1. 0.354 ± 1.96 × 0.048
2. 0.354 ± 1.96 × 0.0047
3. 0.354 ± 0.048
4. 0.048 ± 1.96 × 0.354

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Correct Answer - Option 2 : 0.354 ± 1.96 × 0.0047

Given

Population size = n = 100

Standard deviation = s = 0.048

Sample size = N = 2000

Confidence interval = 95% for 2000 ball bearings

Average diameter of 2000 balls = 0.354

Formula used

Sx = s/√n(√(N - n)/(N - 1)

Calculation

The population is finite and the sample size is large relative to population size we will have to use the finite population correction factor in calculating.

⇒ The population is unknown, since sample is large (n =100) the distribution of X is approximately normal.

⇒ Sx = 0.048√100[(2000 - 100)/(2000 - 1)

⇒ 0.048/10[(1900/1999) = 0.0047

∴ The 95% CI for the average diameter =  0.354 ± (1.96)(0.0047) 

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