A production process for filling orange juice containers labeled as 64 ounces is monitored for the actual amount of juice in the container. The process is designed such that 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. The process is monitored by randomly selecting 24 containers every hour and measuring the actual amount of juice in the containers. An increase in the standard 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.

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 α = .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?

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64.37 64.26 64.22 64.42 64.13 64.44 64.64 64.19 6385 64.17 64.2 64.23 64.64 64.12 63.98 64.34 64.20 64.31 64.15 64.09 64.33 64.19 64.57 64.19