Answer to Question #242971 in Statistics and Probability for Viraj Rambhia

Question

From the following uniformly distributed data scene calculate the probability w.r.t statement. The weekly output of a steel mill is a uniformly distributed random variable that lies between 110 and 175 metric tons.

1. Compute the probability that the steel mill will produce more than 150 metric tons next week.

2. Determine the probability that the steel mill will produce between 120 and 160 metric tons

Answer 1

$$f(x)=\begin{cases} \dfrac{1}{175-110}, & 110\leq x\leq 175 \\ 0 & elsewhere \end{cases}$$

1.

$$P(X>150)=\displaystyle\int_{150}^{175} \dfrac{1}{65}dx=\dfrac{1}{65}[x]\begin{matrix} 175 \\ 150 \end{matrix}$$

$$=\dfrac{25}{65}=\dfrac{5}{13}$$

2.

$$P(120\leq X\leq 160)=\displaystyle\int_{120}^{160} \dfrac{1}{65}dx=\dfrac{1}{65}[x]\begin{matrix} 160 \\ 120 \end{matrix}$$

$$=\dfrac{40}{65}=\dfrac{8}{13}$$