Statistics Homework Solutions 94

# Statistics Homework Solutions 94 - 94 CHAPTER 4 Â 0 25 3 e...

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Unformatted text preview: 94 CHAPTER 4 Â¡ 0 25 3 e 0 5276 Â¢ Â¡ 1 Â¡ Â¡Â¥ 3 Â¨ (c) P X Â¤ Â¡ Â¡ Â¤ 0 5, so e 0 5. Â¨ Â¡ 2 7726 microns. Â¨ Â¡Â¥ Â¤ Â¨ Â¡ Â¨ Â¡ 5 5452 microns. Â¨ Â¤ Â¨ Â¡ 0 01. 18 4207 microns. Â¨ Â¡ Â¡Â¥ Â¤ Â¨ Â¡ Solving for x99 yields x99 0 99, so e Â¨ e 1 0 75. Â¡ Â¡ x99 x99 0 25x99 Â¨ Â¤ Â¨ PT 0 25x99 Â¡Â¥ Â¡Â¥ (g) Let x99 be the 99th percentile. Then P T Â¨ Â¡ Solving for x75 yields x75 0 75. 0 25. 0 75, so e Â¡ e x75 Â¨ 1 Â¤ x75 0 25x75 Â¨ Â¡ PT 0 25x75 Â¡Â¥ Â¤ (f) Let x75 be the 75th percentile, which is also the third quartile. Then P T Â¨ Â¡ Solving for m yields m Â¨ e Â¡ Â¡Â¥ 1 Â¨ Â¡ m 0 5. 0 25m Â¤ PT m Â¡Â¥ Â¡ (e) Let m be the median. Then P T 0 25m 0 0639 Â¨ 0 25 11 e 1 Â¢ 1 Â¡Â¥ 11 Â¨ (d) P X 5. (a) Let X be the number of transistor that last longer than 8 months. The probability that a transistor lasts longer than 8 months is 0.2019. 1 1 Â¤Â¥ 10! 0 2019 1! 10 1 ! 0 2019 Â¡ Â¨ Â¤ Â¥ Â¡ 0 Â¨ 10 1 2 Â¤ Â¥ Â¤ Â¡ Â¡ Â¨ Â¥ Â¥ Â¡ Â¤ Â¤Â¥ Â¡ Â¨ Â¡ Â¨ Â¤Â¥ Â¡ Â¥ Â¡ Â¨ Â¤ Â¤ Â¡ Â¥ Â¤ Â¡ Â¡ Â¡ Â§ Â¤ Â¡ Â¡ Â¤ Â¡ Â¥ Â¡ Â¤ Â¡ Â¥ 1 Â¥ 0 PX 1 PX 2 10! 0 2019 0 1 0 2019 10 0! 10 0 ! 10! 0 2019 2 1 0 2019 10 2! 10 2 ! Â¥ PX Â¤ 1  3 Â¨ PX Bin 10 0 2019 . Â¥ Therefore X 0 3279 Â¨ Â¡ (b) Let T be the lifetime of a transistor, in months. The probability that a transistor fails before 10 months is P T 10 P T 10 1 e 0 2 10 0 86466. Therefore X Bin 10 0 86466 . Â¡ Â¢ Â¤ 10 1 Â¡ Â¥ 10! 0 86466 10! 10 10 ! 0 86466 Â¨ Â¨ Â¤ Â¥ Â¡ Â¤ Â¢ 10 9 Â¥ Â¡ Â¥ Â¨ Â¡ Â¡Â¥ Â¡ Â¥ 0 86466 10 10 Â¨ Â¤ Â¨ Â¤Â¥ Â¡ Â¨ Â¤ Â¤ Â¢Â¥ Â¥ Â¡ Â¡Â¥ Â¡ Â¤ Â¡ Â¡ Â¤ 0 5992 Â¤ 9 P X 10 10! 0 86466 9 1 9! 10 9 !  PX Â¨ Â¨ Â¡ Â¤ Â¥ Â¡ 8 Â¥ Â¡ PX Â¤ ...
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