Answer
No, an investigation is not necessary.
Work Step by Step
n = 800 and p = 0.05
Expected value:
$E(X)=μ_X=np=800\times0.05=40$
Standard deviation:
$σ_X=\sqrt {np(1-p)}=\sqrt {800\times0.05(1-0.05)}=\sqrt {800\times0.05\times0.95}=6.164$
Now, notice that $np(1-p)=800\times0.05\times0.95=38\gt10$. So, according to the given rule on page 343 (blue rectangle) the probability histogram is bell shaped. And, since it is bell shaped, there is a probability of 95% that the number of successes is between $μ_X-2σ_X=40-2\times6.164=27.672$ and $μ_X+2σ_X=40+2\times6.164=52.328$. But, 51 is between 27.627 and 52.328. It would be unusual if more than 52 visitors have died or less than 28. (See Empirical Rule on page 148)
