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Tut sol week8

# Tut sol week8 - BES Tutorial Sample Solutions S1/10 WEEK 8...

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1 BES Tutorial Sample Solutions, S1/10 WEEK 8 TUTORIAL EXERCISES (To be discussed in the week starting April 26) 1. A machine produces sausages with a mean length of 15cm and a standard deviation of 1.5cm. A random sample is taken of 36 sausages made by the machine. What is the probability that the sample mean length of these sausages is greater than 14.8cm? Let = X length of sausage X ) ) 5 . 1 ( , 15 ?( 2 Since n=36 is large we can invoke the central limit theorem X 36 ) 5 . 1 ( , 15 2 N approximately Then 7881 . 0 2881 . 0 5 . 0 ) 8 . 0 0 ( 5 . 0 ) 8 . 0 ( ) 6 5 . 1 ( 15 8 . 14 ) 8 . 14 ( = + = < < + = > = > = > Z P Z P Z P X P 2. Suppose a normally distributed random variable X has a mean of 50 and a variance of 100. Also suppose a sample of size 16 is drawn from this population. Calculate the following probabilities: (a) P( X > 55) 3085 . 0 1915 . 0 5 . 0 ) 5 . 0 ( 10 50 55 ) 55 ( = = > = > = > Z P Z P X P

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2 (b) X ~ ) 16 100 , 50 ( N 0228 . 0 4772 . 0 5 . 0 ) 2 0 ( 5 . 0 ) 2 ( 4 10 50 55 ) 55 ( = = < < = > = > = > Z P Z P Z P X P (c) ) 55 40 ( < < X P 5328 .. 0 1915 . 0 3413 .. 0 ) 5 . 0 0 ( ) 1 0 ( ) 5 . 0 1 ( 10 50 55 10 50 40 ) 55 40 ( = + = < < + < < = < < = < < = < < Z P Z P Z P Z P X P (d) ) 55 40 ( < < X P 9772 . 0 4772 . 0 5 ... 0
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Tut sol week8 - BES Tutorial Sample Solutions S1/10 WEEK 8...

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