91Ó°ÊÓ

The powder specimen has exactly 10anthrax spores.

The number of anthrax spores follows an approximate uniform distribution between 0 and 10.

Let, X denote the number of anthrax spores

X follows a uniform distribution.

The p.d.f of X is given by,

$$\begin{gathered} f\left(x\right)=\frac{1}{d-c};c≤x≤d \\ =\frac{1}{10-0};≤x≤10 \\ =\frac{1}{10} \end{gathered}$$

The probability that 8 or fewer anthrax spores are detected in the powder specimen is $P\left(X≤8\right)$.

$$\begin{gathered} P\left(X≤8\right)={∫}_0^{8}f\left(x\right)dx \\ ={∫}_0^8\frac{1}{10}dx \\ =\frac{8}{10} \\ =0.8 \end{gathered}$$

Hence, the probability that 8 or fewer anthrax spores are detected in the powder specimen is 0.8 .

The probability that between 2 and 5 anthrax spores are detected in the powder specimen is$P\left(2≤X≤5\right)$ .

$$\begin{gathered} P\left(2≤X≤5\right)={∫}_2^{5}f\left(x\right)dx \\ ={∫}_2^5\frac{1}{10}dx \\ =\frac{\left(5-2\right)}{10} \\ =\frac{3}{10} \\ =0.3 \end{gathered}$$

Hence, the probability that between 2 and 5 anthrax spores are detected in the powder specimen is. 0.3 .