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[-I2.65 Points] DETAILS BBU N DERSTAT1 2 6.3.0275. MY NOTES | ASK YOU R TEACHER Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.0 millimeters (mm) and a standard deviation of 1.2 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.) m USE SALT (a) the thickness is less than 3.0 mm (b) the thickness is more than 7.0 mm (c) the thickness is between 3.0 mm and 7.0 mm [-l2.65 Points] DETAILS BBUNDERSTAT12 6.3.030.M|.S. MY NOTES | ASK YOUR TEACHER Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 28 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal. IA USE SALT (a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.) % (b) If Accrotime does not want to make refunds on more than 12% of the watches it makes, how long should the guarantee period be (to the nearest month)? months [l2.65 Points] DETAILS BBU N DERSTAT1 2 6.5.0145. MY NOTES | ASK YOU R TEACHER Suppose the heights of 18year-old men are approximately normally distributed, with mean 73 inches and standard deviation 4 inches. m USE SALT (a) What is the probability that an 18-year-old man selected at random is between 72 and 74 inches tall? (Round your answer to four decimal places.) (b) If a random sample of thirteen 18-year-old men is selected, what is the probability that the mean height)? is between 72 and 74 inches? (Round your answer to four decimal places.) (c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this? 0 The probability in part (b) is much higher because the standard deviation is smaller for the distribution. 0 The probability in part (b) is much higher because the standard deviation is larger for the x distribution. 0 The probability in part (b) is much higher because the mean is larger for the 7 distribution. 0 The probability in part (b) is much lower because the standard deviation is smaller for the 7 distribution. 0 The probability in part (b) is much higher because the mean is smaller for the x distribution