A small business ships specialty homemade candies to anywhere in the world.Past records indicate that the weight of orders is normally distributed.Suppose a random sample of 16 orders is selected and each is weighed.The sample mean was found to be 110 grams with a standard deviation of 14 grams.The 90% confidence interval for the true mean weight of orders is ________________________ .

Question

Quizplus · Accepted Answer

The 90% confidence interval for the true mean weight of orders can be calculated using the formula for the confidence interval of the mean with known standard deviation: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the confidence level (for 90%, $z = 1.645$), $\sigma$ is the standard deviation, and $n$ is the sample size. Plugging in the given values: $110 \pm 1.645\frac{14}{\sqrt{16}}$ results in the interval $103.87$ to $116.14$ grams.

A Small Business Ships Specialty Homemade Candies to Anywhere in the World.Past