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1. Consider a normal distribution with mean 31 and standard deviation 5. What is the probability a value selected at random from this distribution is greater than 31? (Round your answer to two decimal places.) 2.Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) u = 15.5; 0 = 3.5 e(10 120) = 5.Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) u = 2.8; 0 = 0.30 P(x 2 2) = 6.Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.9 millimeters (mm) and a standard deviation of 1.0 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.) (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 7. Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 43.6 months and a standard deviation of 8.7 months. (a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.) % (b) If Quick Start does not want to make refunds for more than 5% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)? months