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 95 percent confidence interval for μ. A)[71.25,78.75] B)[72.23,77.77] C)[47.28,102.72] D)[72.67,77.33]

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for the population mean with a known population standard deviation:

CI = x̄ ± z*(σ/√n)
Where:
x̄ = sample mean = 75 lbs
σ = population standard deviation = 100 lbs
n = sample size = 50
z = z-score for the desired confidence level. For a 95% confidence level, z = 1.96 (from the standard normal distribution table).

Plugging in the values, we get:
CI = 75 ± 1.96*(100/√50) ≈ [72.23, 77.77]

Therefore, the best choice is B.

The Weight of a Product Is Measured in Pounds