# Week 5 Res/341 Exercises

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Week 5 RES/ 341 Chapter Exercises: 7.54 The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 579 MPa with a standard deviation of 14 MPa. (a) What is the probability that a randomly chosen sample of glass will break at less than 579 MPa? (b) More than 590 MPa? (c) Less than 600 MPa? (Data are from Science 283 [February 26, 1999], p. 1296.) A) What is the probability that a randomly chosen sample of glass will break at less than 579 MPa? z(579) = (579-579)/14 = 0 P(x &lt; 579) = P(z&lt;0) = 0.5000 B) More than 590 MPa? z(590) = (590-579)/14= 11/14= 0.7857 P(x&lt;500) = P(z&lt; 0.7857) = 0.2160 C) Less Than 600 MPa? z(600) = (600-579)/14 = 21/14= 3/2 P(x&lt;600) = =P(z&lt;3/2) = 0.9332 7.56 In a certain microwave oven on the high power setting, the time it takes a randomly chosen kernel of popcorn to pop is normally distributed with a mean of 140 seconds and a standard deviation of 25 seconds. What percentage of the kernels will fail to pop if the popcorn is cooked for (a) 2 minutes? (b) Three minutes? (c) If you wanted 95 percent of the kernels to pop, what time would you allow? (d) If you wanted 99 percent to pop? A) 2 minutes = 120 seconds z(120) = 120-150)/25= -30/25 = -6/5= -1.2 P(z&gt;-1.2) = 0.1151 B) 3 minutes = 180 seconds z(180) = (180-150)/25=30/25 = 6/5 = 1.2 P(z&gt;1.2) = 0.1151 C) If you want 95% of the kernels to pop, what time would you allow? (.95) = 1.645 x-150 = 25*1.645 x = 41.12 = 150= 191.12 seconds x = 3 minutes and 11.12 seconds D) If you want 99% to pop… (.99) = 2.326 2.326 = (x-150)/25 x = 25* 2.326 + 150 x= 208.16 seconds x = 3 minutes and 28.16 seconds 8.46 A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241