The weight of a product is measured in pounds.A sample of 50 units is taken from a batch.The sample yielded = 75 lbs. ,and we know that σ² = 100 lbs.Calculate a 90 percent confidence interval for μ. A)[73.19,76.81] B)[51.74,98.26] C)[72.67,77.33] D)[67.50,82.50]

Question

Quizplus · Accepted Answer

We can use the formula for the confidence interval:
CI = sample mean ± (z-score)(standard error)
where the standard error is calculated as σ/√n and the z-score can be found using a z-table or calculator for a 90% confidence level, which corresponds to a z-score of 1.645.

Plugging in the given values, we get:
CI = 75 ± (1.645)(100/√50)
CI = [72.67, 77.33]

Therefore, the best choice is (C) [72.67, 77.33].

The Weight of a Product Is Measured in Pounds