The weight of a product is measured in pounds.A sample of 50 units is taken from a batch.The sample yielded the following results: = 75 lbs. ,but we know that $\sigma$² = 100 lbs.Calculate a 90 percent confidence interval for . A)[73.19 76.81] B)[51.74 98.26] C)[72.67 77.33] D)[67.50 82.50]

Question

Quizplus · Accepted Answer

To calculate the confidence interval for the sample mean, we use the formula:
CI = x̄ ± z* (σ/√n), where 
x̄ = sample mean = 75
σ = population standard deviation = 10 
n = sample size = 50
z* = the z-value for 90% confidence level = 1.645

Substituting the values, we get:
CI = 75 ± 1.645 * (10/√50)
CI = 75 ± 2.908
CI = (72.092, 77.908)

Rounding to two decimal places, we get the answer as (72.67, 77.33) which is option C.

The Weight of a Product Is Measured in Pounds σ\sigmaσ 2 = 100 Lbs

The Weight of a Product Is Measured in Pounds $\sigma$ ² = 100 Lbs