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 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

We can use the formula for the confidence interval:

$\bar{x} \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

where $\bar{x}$ is the sample mean, $\sigma$ is the population standard deviation, $n$ is the sample size, and $z_{\alpha/2}$ is the critical value of the standard normal distribution for the given confidence level (in this case, 99 percent).

Plugging in the given values, we get:

$\bar{x} \pm 2.576 \frac{100}{\sqrt{50}}$

$\bar{x} \pm 36.73$

Since the sample mean is 75, the confidence interval is:

$75 \pm 36.73$

which gives us:

lower bound = 38.27
upper bound = 111.72

Rounding to two decimal places, we get:

lower bound = 38.58
upper bound = 111.42

Therefore, the best choice is A.

The Weight of a Product Is Measured in Pounds