The breaking strength of a rivet has a mean value of 9,900 psi and a standard deviation of 496 psi. A USE SALT (a) What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,800 and 10,100? (Round your answer to four decimal places.) 0.8945 (b) If the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given information? Explain your reasoning. O Yes, the probability in part (a) can still be calculated from the given information. O No, n should be greater than 30 in order to apply the Central Limit Theorem. O No, n should be greater than 20 in order to apply the Central Limit Theorem. O No, n should be greater than 50 in order to apply the Central Limit Theorem.

Question
The breaking strength of a rivet has a mean value of 9,900 psi and a standard deviation of 496 psi.
A USE SALT
(a) What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,800 and 10,100? (Round your
answer to four decimal places.)
0.8945
(b) If the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given information? Explain your
reasoning.
O Yes, the probability in part (a) can still be calculated from the given information.
O No, n should be greater than 30 in order to apply the Central Limit Theorem.
O No, n should be greater than 20 in order to apply the Central Limit Theorem.
O No, n should be greater than 50 in order to apply the Central Limit Theorem.
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Transcribed Image Text

The breaking strength of a rivet has a mean value of 9,900 psi and a standard deviation of 496 psi. A USE SALT (a) What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,800 and 10,100? (Round your answer to four decimal places.) 0.8945 (b) If the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given information? Explain your reasoning. O Yes, the probability in part (a) can still be calculated from the given information. O No, n should be greater than 30 in order to apply the Central Limit Theorem. O No, n should be greater than 20 in order to apply the Central Limit Theorem. O No, n should be greater than 50 in order to apply the Central Limit Theorem.

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