Question

2. In 1904, William Sealy Gosset was a statistician working for Dublin's Guinness Brewing Company. At that time, the company had issues to reach suitable fermentation. The problem was due to the inadequate quantity of yeast to prepare the mash for the fermentation process. Yeast cells were typically dispersed in a small volume and an aliquot was sampled to be observed under the microscope so that the count of the cells could be carried out. The cells are suspended in a medium at a concentration of 10 cells per mL: if an aliquot of 1 mL is withdrawn, how would you calculate the probability that exactly 8 particles are observed? (3 points)

Answer 1

It is given that

concentration of medium , $\lambda =10$

the number of particles , x=8

Poisson distribution $P(X)=\frac{e^{-\lambda }*\lambda ^x}{x!}$

$P(X)=\frac{e^{-10 }*10 ^8}{8!}$

$P(X)=\frac{e^{-10 }*10 ^8}{8*7*6*5*4*3*2*1}$

$P(X)=\frac{4539.99}{40320}$

$P(X)=0.1126$

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