Question

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

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 :

• $μ ± Z_{crit}(\frac{σ}{\sqrt{n}})$
• σ = 50
• Zcrit 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 = $1.96(\frac{50}{\sqrt{12}}) = 28.290$

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)

Learn more :https://brainly.com/question/25704508