SOLUTION: Question 6 i) If X follows a Poisson distribution, written X ~ Pn(3), a) Write down the probability distribution function for the random variable X. b) Find i. P(X = 0)

Question 1055827: Question 6
i) If X follows a Poisson distribution, written X ~ Pn(3),
a) Write down the probability distribution function for the random variable X.
b) Find
i. P(X = 0) ii. P(X = 3) iii. P(X > 1)
iv. P(X = 3 | X > 1)
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.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
F(x)=exp^(-3)*3^x/x!
For x=0, P(x)=exp^(-3)=0.0498
For x=3, exp (-3)*27/6=0.2240
for x> 1
prob x=1 is exp^(-3)*3=0.1494
Prob x>1 is 1-(0.0498+0.1494)=0.8008
The z value is (x-mean)/sd
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)
The probability that z is between those two values of -2.5 and 1.6667 is 0.9460.
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