Probability 53061

One hundred people work in the office. Each of them spends an average of 25 minutes daily on the phone. A working day has 8 hours.
What is the probability that ten workers will be on the phone simultaneously in one day?

Correct answer:

p =  0.0206

Step-by-step explanation:

$$\begin{gathered} t_1=25\text{min}\to \text{h}=25:60\text{h}=0.41667\text{h} \\ {t}_2=8\text{h} \\ {p}_1=\frac{t_1}{t_2}=\frac{\frac{5}{12}}{8}=\frac{5}{96}\doteq 0.0521 \\ n=100 \\ p=\left(\genfrac{}{}{0ex}{}{n}{10}\right)\cdot p_1^{10}\cdot (1-p_1{)}^{n-10}=(\genfrac{}{}{0ex}{}{100}{10})\cdot 0.0521^{10}\cdot (1-0.0521{)}^{100-10}=17310309456440\cdot 0.0521^{10}\cdot 0.9479^{90}=0.0206 \end{gathered}$$

Try another example