A local company makes a candy that is supposed to weigh 1.00 gram.A random sample of 25 pieces of candy produces a mean of 0.996g with a standard deviation of 0.004g.If candy weight is normally distributed,the 98% confidence interval for the mean weight of all such candy would be _____.
A)[0.9645,1.0275]
B)[0.9956,0.9964]
C)[0.9860,1.0060]
D)[0.9940,0.9980]
E)[0.9942,0.9978]

Question

Quizplus · Accepted Answer

The 98% confidence interval for the mean weight of all such candy can be calculated using the formula for the confidence interval of the mean: $\bar{x} \pm Z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the confidence level (in this case, 98%), $\sigma$ is the standard deviation, and $n$ is the sample size. Given $\bar{x} = 0.996g$, $\sigma = 0.004g$, and $n = 25$, and knowing that the Z-score for a 98% confidence level is approximately 2.33, the calculation yields the interval [0.9940, 0.9980], which matches option D.

A Local Company Makes a Candy That Is Supposed to Weigh