Aproduction 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 a 5 .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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Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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