Test 2.pdf - Name Stat 131 Test 2 Show all work Do in...

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Name ____________________________ Stat 131 Test 2 Show all work. Do in pencil . Don’t round until your final answer. Show as many decimals as practical to clearly indicate your final answer. Circle your final answer. 1 otherwise , 0 1 , ) ( 2 x ae x f x Calculate a so that f ( x ) is a density function. (6 points) Calculate P( X ≤ 1.5). (6 points) 2 otherwise , 0 2 , 2 ) ( 4 x x c x f Calculate E[ X ]. (8 points)
3 Piston rods manufactured by a company have lengths that are normally distributed with mean 75.45 mm and variance 0.04 mm 2 . These rods will meet specifications if their lengths are between 75 and 76 mm. a Calculate the probability that a single rod, sampled at random, meets specifications. (8 points) b Calculate the probability a randomly picked rod has length greater than 75.25. (6 points) 4 The lifetime of a particular \$150 cell phone that is exponentially distributed with a mean of three years. The manufacturer will pay a full refund if the phone fails in the first year. The manufacturer will refund half of the value of the phone if it fails in the second year. Calculate how much the manufacturer will expect to refund for one phone. (10 points)