Answer
a. μ=λ=3.7
P(x\leq ) =$\frac{3.7^{0}e^{-3.7}}{0!}$+$\frac{3.7^{1}e^{-3.7}}{1!}$ = 0.1162
b.i.$P(1\leq x \leq 4)$ =$\frac{3.7^{1}e^{-3.7}}{1!}$+$\frac{3.7^{2}e^{-3.7}}
{2!}$+$\frac{3.7^{3}e^{-3.7}}{3!}$+$\frac{3.7^{4}e^{-3.7}}{4!}$ =0.6625
ii. $P(x\geq6)$ =1-$P(0\leq x \leq 5)$ = 0.8301
iii.$P(x\leq3)$ =$\frac{3.7^{0}e^{-3.7}}{0!}$+$\frac{3.7^{1}e^{-3.7}}{1!}$+$\frac{3.7^{2}e^{-3.7}}
{2!}$+$\frac{3.7^{3}e^{-3.7}}{3!}$ =0.4942
Work Step by Step
see above