st422%20hw01%20solution

# st422%20hw01%20solution - Homework 1 Solutions 7.1 ℴ =1 a...

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Unformatted text preview: Homework 1: Solutions 7.1 ℴ =1 a) P(|Ybar- μ |<=.3) = P(-.3/( ℴ / √ (n))<=(Ybar- μ)/( ℴ / √ (n))<=.3/( ℴ / √ (n)) = P(-.3/(1/4)<=z<=.3/(1/4)) = P(-1.2<=z<=1.2) = 1-2P(Z>=1.2) =1-2(.1151) = .7698 Proceeding similarly, b) n=25 P(|Ybar- μ |<=.3) =1-2P(Z>=1.5) =1-2(.0668) = .8664 c)n=36 P(|Ybar- μ |<=.3) =1-2P(Z>=1.8) =1-2(.0359) = .9282 d)n=49 P(|Ybar- μ |<=.3) =1-2P(Z>=2.1) =1-2(.0179) = .9642 c)n=36 P(|Ybar- μ |<=.3) =1-2P(Z>=1.8) =1-2(.0359) = .9282 c)n=64 P(|Ybar- μ |<=.3) =1-2P(Z>=2.4) =1-2(.0082) = .9836 c) The probability increases with n d)Yes 7.2 ℴ=2 a) n=9 P(|Ybar- μ |<=.3) =1-2P(Z>=.45) =1-2(.3264) = .3472 a) n=25 P(|Ybar- μ |<=.3) =1-2P(Z>=.75) =1-2(.2266) = .5468 a) n=36 P(|Ybar- μ |<=.3) =1-2P(Z>=.9) =1-2(.1841) = .6318 a) n=49 P(|Ybar- μ |<=.3) =1-2P(Z>=1.05) =1-2(.1469) = .7062 a) n=64 P(|Ybar- μ |<=.3) =1-2P(Z>=1.2) =1-2(.1151) = .7698 c) n increases with probability d)probabilities are smaller compared to the previous case 7.5 P(|Ybar- μ |<=.5) =1-2P(Z>2.5) =1-2(.0062) = .9876 7.6 7....
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st422%20hw01%20solution - Homework 1 Solutions 7.1 ℴ =1 a...

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