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
A) 103.87 to 116.14 grams.
B) 86.046 to 133.954 grams.
C) 99.5 to 120.5 grams.
D) 102.55 to 117.45 grams.
E) 103.14 to 116.86 grams.

Question

Quizplus · Accepted Answer

The correct 90% confidence interval is 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 desired confidence level (for 90%, $z = 1.645$), $\sigma$ is the standard deviation, and $n$ is the sample size. Plugging in the given values ($\bar{x} = 110$, $\sigma = 14$, $n = 16$), we get the interval 103.87 to 116.14 grams.

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