document.write( "Question 1055827: Question 6
\n" ); document.write( "i) If X follows a Poisson distribution, written X ~ Pn(3),
\n" ); document.write( "a) Write down the probability distribution function for the random variable X.
\n" ); document.write( "b) Find
\n" ); document.write( "i. P(X = 0) ii. P(X = 3) iii. P(X > 1)
\n" ); document.write( "iv. P(X = 3 | X > 1)
\n" ); document.write( "ii. At a Junior athlete’s competition, it is found that the times taken for children aged 10 to sprint the 50 metres race are normally distributed with a mean of 15.6 seconds and standard deviation of 0.24 seconds. Find the probability the time taken for a 14 year old at the meet to sprint the 50 metres is between 15 and 16 seconds. \n" ); document.write( "

Algebra.Com's Answer #671006 by Boreal(15235) $\"\"$ $\"About$

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F(x)=exp^(-3)*3^x/x!
\n" ); document.write( "For x=0, P(x)=exp^(-3)=0.0498
\n" ); document.write( "For x=3, exp (-3)*27/6=0.2240
\n" ); document.write( "for x> 1
\n" ); document.write( "prob x=1 is exp^(-3)*3=0.1494
\n" ); document.write( "Prob x>1 is 1-(0.0498+0.1494)=0.8008
\n" ); document.write( "The z value is (x-mean)/sd
\n" ); document.write( "With sd of 0.24 sec, it is 2.5 sds to the left of the mean (-z) and +1.6667 sd to the right of the mean (positive)
\n" ); document.write( "The probability that z is between those two values of -2.5 and 1.6667 is 0.9460. \n" ); document.write( "

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