Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 12 boxes. It is reasonable to assume that the population is approximately normal.13.09 14.53 13.18 13.19 13.17 13.0913.12 14.53 13.02 13.01 13.08 13.09Send data to ExcelPart: 0 / 20 of 2 Parts CompletePart 1 of 2Construct a 99% confidence interval for the mean weight. Round the answers to three decimal places. <<μ

A food company claims that the average weight of their cereal boxes is 500 grams. To test this claim, a consumer protection agency randomly selects 20 boxes and finds that the average weight of the selected boxes is 495 grams with a standard deviation of 10 grams. Test the company's claim at the 1% level of significance.

A random sample of 12 items is taken and is found to have a meanweight of 50 grams and a standard deviation of 9 gramsWhat is the mean weight of population1. with 95% confidence2. with 99% confidence

The amount of cereal in boxes, packed by a particular machine, is normally distributed with mean µ gram andstandard deviation 5 gram. If the advertised weight of a box is 500 gram, find(i) the proportion of boxes that will be underweight (i.e. weight less than 500 gram) when µ = 505;(ii) the value of µ required to ensure that only 1% of the boxes are underweight.(b) As a check on the setting of the machine a random sample of four boxes is chosen and the setting changed if theaverage weight of the four boxes is less than 500 gram. Find the probability that the setting of the machine ischanged when µ = 505.

A random sample of 120 apricots is selected from trees in a Hawkes Bay orchard and the weight of each apricot is measured, giving mean of 42 grams and SD of 12 grams.This information is to be used to calculate a 95% confidence interval for the true mean weight of apricots grown on trees in this Hawkes Bay orchard.Use the drop-down menus to identify if the following conditions for constructing this confidence interval are satisfied or not.The sample is representative of the population.AnswerThe sampling distribution of the sample mean is normal.

Let's shake on it: A random sample of 12-ounce milkshakes from 11 fast-food restaurants had the following number of calories.375 608 473 476 504 510 472700 642 591 580 Send data to ExcelAssume the population standard deviation is =σ85.Part 1 of 3(a) Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.It is necessary to check whether the population is approximately normal because ▼the sample size is less than or equal to 30.Part 2 of 3(b) Following is a dotplot of these data. Is it reasonable to assume that the population is approximately normal?350400450500550600650700It ▼is reasonable to assume that the population is approximately normal.Part: 2 / 32 of 3 Parts CompletePart 3 of 3(c) If appropriate, construct an 80% confidence interval for the mean calorie count for all 12-ounce milkshakes sold at fast-food restaurants. Round the answers to at least two decimal places.An 80% confidence interval for the mean calorie count for all 12-ounce milkshakes sold at fast-food restaurants is <<μ.