Answer to Question #267303 in Statistics and Probability for John

Question

Upon studying low bids for shipping contracts, a microcomputer manufacturing company finds that intrastate contract have low bids that are uniformly distributed between 20 and 25, in units of thousands of dollars. Find the probability that the low bids on the next intrastate shipping contract

(A) is below k22000

(B) is in excess of k24000

Answer 1

$$f(x) = \begin{cases} \dfrac{1}{25-20}, &20\leq x\leq2 \\ 0, &elsewhere \end{cases}$$

(A)

$$P(X<22)=\displaystyle\int_{20}^{22} \dfrac{1}{25-20}dx= \dfrac{1}{5}[ x]\begin{matrix} 22 \\ 20 \end{matrix}$$

$$= \dfrac{1}{5}(22-20)= \dfrac{2}{5}=0.4$$

(B)

$$P(X>24)=\displaystyle\int_{24}^{25} \dfrac{1}{25-20}dx= \dfrac{1}{5}[ x]\begin{matrix} 25 \\ 24 \end{matrix}$$

$$= \dfrac{1}{5}(25-24)= \dfrac{1}{5}=0.2$$