# hw5 - STA 103: Lab 4 Prof. Baines (Fall 2012) Assigned:...

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Homework #5 - Solution Page 1 of 5 STAT 350 – Spring 2009 Homework #5 Solution covers through Lecture I Text Exercises Chapter 5, Problems # 46b&c, 50, 52, 54 Chapter 7, Problem # 30 5.46 Let X = the inside diameter of a randomly selected piston ring in cm. E(X) = 12, SD(X) = 0.04 b.   12 EX   0.04 0.005 64 SD X SD X n c. The mean of a random sample of size 64 5.50 a. 50 ,   1 0.1 100 SD X SD X n 49.75 50 50 50.25 50 49.75 50.25 0.1 0.1 0.1 2.5 2.5 (2.5) ( 2.5) 0.9938 0.0062 0.9876 X PX P PZ       b. 49.8 ,   1 0.1 100 SD X SD X n 49.75 49.8 49.8 50.25 49.8 49.75 50.25 0.1 0.1 0.1 0.5 4.5 (4.5) ( 0.5) 1 0.3085 0.6915 X P 5.52 a. 50 ,   1.5 0.5 9 SD X SD X n 50 52 50 52 4 0 0.5 0.5 X P  On the standard normal table, the best you can say is the probability is approx. zero, the actual probability is about 0.000032 b. 50 ,   1.5 0.23717 40 SD X SD X n 50 52 50 52 8.43 0 1.5 40 1.5 40 X P Even statistical packages will return this probability as 0.

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Homework #5 - Solution Page 2 of 5 5.54 a. E(X) = 0(0.8) + 1(0.1) + 2(0.05) + 3(0.05) = 0.35 Var(X) = (0-0.35) 2 (0.8) + (1-0.35) 2 (0.1) + (2-0.35) 2 (0.05) + (3-0.35) 2 (0.05) = 0.6275 SD(X) = 0.6275 = 0.79215 b.   0.35 EX  ,    0.79215 0.09902 64 SD X SD X n c. 0.35 1 0.35 16 . 5 6 0 0.09902 0.09902 X PX P PZ      The actual answer is about 2.7 × 10 -11 7.30 22 4.89 6.43 26.99 35.76 1.96 68 74  = (-10.6401, -6.8999) Note: (6.8999, 10.6401) is also acceptable, this is just the 95% CI for 21 instead of 12 Then answer the following problems: 1. The commercial says, “4 out of 5 dentists recommend sugarless gum for their patients that chew gum.” Assume that what this actually means is that if you randomly select a dentist, the probability that he (or she) would recommend sugarless gum is 4/5. a. You randomly select 17 dentists from a professional directory. You call them and ask if they would recommend sugarless gum for their patients that chew gum. Let p 1 denote the proportion of dentists in your sample that answer “yes.” Let X = the number of dentists in the sample that say yes.
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## This note was uploaded on 02/16/2010 for the course STAT 350 taught by Professor Staff during the Spring '08 term at Purdue.

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hw5 - STA 103: Lab 4 Prof. Baines (Fall 2012) Assigned:...

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