A soft-drink bottler purchases glass bottles from a vendor. The bottles are required to have internal pressure strength of at least 150 pounds per square inch (psi). A prospective bottle vendor claims that its production process yields bottles with mean internal pressure strength of 157 psi and standard deviation of 3 psi. The bottler strikes an agreement with the vendor that permits the bottler to sample from the vendor's production process to verify the vendor's claim. The bottler obtains a random sample of 64 bottles. If the mean internal pressure strength of the sample falls below K, the bottler will conclude the vendor's claim about the mean internal pressure strength to be false. Suppose the bottler is willing to risk a 2% chance of concluding the vendor's claim to be false even if the claim is true. Find the value of K.

Question

Physics

Beau Faulkner

18 January, 20:35

A soft-drink bottler purchases glass bottles from a vendor. The bottles are required to have internal pressure strength of at least 150 pounds per square inch (psi). A prospective bottle vendor claims that its production process yields bottles with mean internal pressure strength of 157 psi and standard deviation of 3 psi. The bottler strikes an agreement with the vendor that permits the bottler to sample from the vendor's production process to verify the vendor's claim. The bottler obtains a random sample of 64 bottles. If the mean internal pressure strength of the sample falls below K, the bottler will conclude the vendor's claim about the mean internal pressure strength to be false. Suppose the bottler is willing to risk a 2% chance of concluding the vendor's claim to be false even if the claim is true. Find the value of K.

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Answers (1)

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Lilliana Ellis · Answer 1

Answer: K = 24 psi

Explanation:

Given: Standard deviation = 3psi

Internal pressure strength = 157psi

Number of random bottle = n=64

K = 3 * square root of 64

K = 3*8=24 psi

If mean internal pressure K fall below K,

157-1.3=155.7psi

At 2%:

0.16*64 = 10.24