The time in hours for a worker to repair an electrical instrument is a Normally distributed random variable with a mean of and a standard deviation of 50. The repair times for 12 such instruments chosen at random are as follows

Answers

Answer 1

Using the confidence interval relation, the confidence interval at 95% would be (189.790 ; 246.370)

The confidence interval could be defined thus :

[tex] μ ± Z_{crit}(\frac{σ}{\sqrt{n}}) [/tex] σ = 50Zcrit at 95% = 1.96

Since we are given the population standard deviation, we the Z distribution :

μ = ΣX / n = (2617 / 12) = 218.08 M.E = [tex] 1.96(\frac{50}{\sqrt{12}}) = 28.290 [/tex]

Substituting the values into the relation :

Lower boundary : 218.08 - 28.290 = 189.790

Upper boundary : 218.08 + 28.290 = 246.370

Hence, the confidence interval is (189.790 ; 246.370)

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