Question

lets practice math
question 3 (34 points)
a random sample of 50 cereal boxes has a mean weight of 475 grams with a standard deviation of 15 grams. calculate the 99% confidence interval for the mean weight of the boxes. the 99% confidence interval is calculated as mean ± (2.58×standard deviation/√# of samples)
the confidence interval is 50 ± 5.47. therefore, we are 99% confident that the true mean weight of the boxes is between 44.52 grams and 55.48 grams.
the confidence interval is 475 ± 10.48. therefore, we are 99% confident that the true mean weight of the boxes is between 499.52 grams and 520.48 grams.
the confidence interval is 475 ± 5.47. therefore, we are 99% confident that the true mean weight of the boxes is between 469.52 grams and 480.48 grams.
the confidence interval is 50 ± 10.48. therefore, we are 99% confident that the true mean weight of the boxes is between 39.52 grams and 60.48 grams.

Explanation:

Step1: Identify given values

Mean = 475, Standard deviation = 15, Number of samples = 50

Step2: Calculate the margin of error

$2.58\times\frac{15}{\sqrt{50}}\approx 2.58\times\frac{15}{7.071}\approx 5.47$

Step3: Find the confidence - interval

The confidence interval is $475\pm5.47$

Answer:

The confidence interval is 475 ± 5.47. Therefore, we are 99% confident that the true mean weight of the boxes is between 469.52 grams and 480.48 grams. (The correct option is the third one in the multiple - choice list)