Answer:
Step-by-step explanation:
The total number of claim is the sum S of 1250 independent random variables,
each having poisson distribution with mean μ = 2
Since the Variance of poisson distribution is equal to its mean ,
the standard deviation of this is
[tex]\sigma= \sqrt{2}[/tex]
By the CLT is follow that S is approximately normal with mean 1250*2 =2500
and standard deviation [tex]\sqrt{1250} *\sqrt{2} =50[/tex]
Hence, the probability to compute is
[tex]P(2350\leq S\leq 2600)=P(\frac{2450-2500}{50} \leq \frac{S-2500}{50} \leq \frac{2600-2500}{50} )\\\\=P(-1<2<2)\\\\=P(2\leq 2)-P(2\leq 1)\\\\=0.977249868-0.15365525\\\\=0.818594614\\\\=0.82[/tex]
