5 A production process for filling orange juice containers

Last updated: 10/31/2023

5 A production process for filling orange juice containers labeled as 64 ounces is monitored or the actual amount of juice in the container The process is designed such that the amount juice in the containers has a normal distribution with a mean of 64 3 ounces and a standard eviation of 15 ounces The process is monitored by randomly selecting 24 containers every our and measuring the actual amount of juice in the containers An increase in the standard 37 54 deviation beyond 15 ounces with the mean remaining at 64 3 ounces will result in a production run with too many underfilled and overfilled containers The following data are the actual amounts of juice in a random sample of 24 containers 64 26 64 22 64 42 64 13 64 44 64 64 64 19 64 12 63 98 64 34 64 20 64 31 64 15 64 09 63 85 64 17 64 21 64 23 64 33 64 19 64 57 64 19 a If the amount of juice in the containers has a normal distribution with a mean of 64 3 ounces and a standard deviation of 15 ounces what proportion of containers filled on the production line will be underfilled contain less than 64 ounces What percentage will be overfilled b Construct a 95 confidence interval on the process standard deviation c Do the data indicate that the process standard deviation is greater than 15 ounces Use a 05 in reaching your conclusion d What is the p value of your test e Is there any indication that the necessary conditions for constructing the confidence interval and conducting the test may be violated f What is the population about which inferences can be made using the given data