The weight of a product is measured in pounds.A sample of 50 units is taken from a recent production.The sample yielded = 75 lb,and we know that σ² = 100 lb.Calculate a 99 percent confidence interval for μ. A) [71.36,78.64] B) [74.25,75.75] C) [38.58,111.42] D) [71.71,78.29]

Question

Quizplus · Accepted Answer

To find the confidence interval for μ, we can use the formula:

CI = X̄ ± Zα/2 (σ/√n)

where X̄ is the sample mean, Zα/2 is the critical value from the standard normal distribution (which is 2.576 for a 99% confidence interval), σ is the population standard deviation, and n is the sample size.

Plugging in the values:

CI = 75 ± 2.576 (10/√50)

CI = 75 ± 3.628

CI = [71.372, 78.628]

Rounding to two decimal places, the answer is (A) [71.36, 78.64].

The Weight of a Product Is Measured in Pounds