process claimed to yield bottles w/ mean int. press. 157 psi, stand. dev. 3 psi

[alexisleigh96]

A soft drink bottler purchases glass bottles from a vendor. The bottles are required to have an internal pressure of at least

pounds per square inch (psi). A prospective bottle vendor claims that its production process yields bottles with a mean internal pressure of

psi and a standard deviation of

psi. The bottler strikes an agreement with the vendor that permits the bottler to sample from the production process to verify the claim. the bottler randomly selects

bottles from the last

produced, measures the internal pressure of each, and finds the mean pressure for the sample to be

psi below the process mean cited by the vendor. (a) Assuming that the vendor is correct in his claim, what is the probability of obtaining a sample mean this far or farther below the process mean?

(b) If the standard deviation were

psi as claimed, but the mean was

psi, what is the probability of obtaining a sample mean of

psi or below?
(c) If the process mean were

psi as claimed, but the standard deviation was

psi, what is the probability of obtaining a sample mean of

psi or below?

 

[Deleted member 4993]

A soft drink bottler purchases glass bottles from a vendor. The bottles are required to have an internal pressure of at least

pounds per square inch (psi). A prospective bottle vendor claims that its production process yields bottles with a mean internal pressure of

psi and a standard deviation of

psi. The bottler strikes an agreement with the vendor that permits the bottler to sample from the production process to verify the claim. the bottler randomly selects

bottles from the last

produced, measures the internal pressure of each, and finds the mean pressure for the sample to be

psi below the process mean cited by the vendor. (a) Assuming that the vendor is correct in his claim, what is the probability of obtaining a sample mean this far or farther below the process mean?

(b) If the standard deviation were

psi as claimed, but the mean was

psi, what is the probability of obtaining a sample mean of

psi or below?
(c) If the process mean were

psi as claimed, but the standard deviation was

psi, what is the probability of obtaining a sample mean of

psi or below?

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[stapel]

typing out the numbers in the images

The numbers in this exercise are hotlinked images. In case the hotlinks break down at some point, here is the text:

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A soft-drink bottler purchases glass bottles from a vendor. The bottles are requires to have an internal pressure of at least 150 pounds per square inch (PSI). A prospective bottle vendor claims that its production process yields bottles with a mean internal pressure of 157 PSI and a standard deviation of 3 PSI.


(a) Assuming that the vendor is correct in his claim, what is the probability of obtaining a sample mean this far, or further, below the process mean?

(b) If the standard deviation were 3 PSI as claimed, but the process mean were 150 PSI, what is the probability of obtaining a sample mean of 156.3 PSI or below?

(c) If the process mean were 157 PSI as claimed, but the standard deviation were 1.7 PSI, what is the probability of obtaining a sample mean of 156.3 PSI or below?