Answer:
t = 45 cubic light years to find a star with this certainty.
Step-by-step explanation:
The Poisson random probability equation is given by:
[tex]P(k events in interval t)=\frac{(\lambda t)^{k}e^{-\lambda t}}{k!}[/tex]
We can use the next equation to quantify how many cubic light years of space must be studied so that the probability of one or more stars exceeds 0.94.
[tex]P(k\ge 1) \ge 0.94[/tex]
[tex]1-f(0)=1-\frac{(\frac{1}{16}*t)^{0}e^{-\frac{1}{16}*t}}{0!}=1-e^{-\frac{1}{16}*t}} \ge 0.94[/tex]
So, here we just need to solve it for t:
[tex]1-e^{-\frac{1}{16}*t}} \ge 0.94[/tex]
[tex]e^{-\frac{1}{16}*t}} \ge 0.06[/tex]
[tex]ln(e^{-\frac{1}{16}*t}}) \ge ln(0.06)[/tex]
[tex]-\frac{1}{16}*t \ge -2.8[/tex]
[tex]t \ge 44.8[/tex]
Therefore t = 45 cubic light years to find a star with this certainty.
I hope it helps you!
