The lengths of nails manufactured at a factory are normally distributed with a mean length of 4.43 cm and a standard deviation of 1.41 cm. For quality control purposes, a random sample of 14 nails is chosen once per day, and measured. Let X be the random variable representing the mean length of the nails. A. Fill in the blank, rounding your answers to 2 decimal places if needed. According to the Central Limit Theorem, X is approximately normal with a mean of _______cm and a standard error of the mean________cm b. Find the z-score associated to a sample with a mean of 4.56 cm, using the sampling distribution. Round your answer to two decimal places. ______ c. Find the probability that a randomly selected sample of 14 nails has a mean length higher than 4.56 cm. Round your answer to 4 decimal places.________
The lengths of nails manufactured at a factory are
A. Fill in the blank, rounding your answers to 2 decimal places if needed. According to the Central Limit Theorem, X is approximately normal with a mean of _______cm and a standard error of the mean________cm
b. Find the z-score associated to a sample with a mean of 4.56 cm, using the sampling distribution. Round your answer to two decimal places. ______
c. Find the
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c. Find the
e. The machine that cuts the nails will be pulled for inspection and repairs if the sample mean of the quality control sample is in the bottom 3% or top 3% of possible sample means. What sample average lengths will trigger a repair? Round your answers to 2 decimal places.
The machine will be pulled for repairs if the quality control sample has a mean length below_______ cm or above_______ cm.
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