Question

consider a uniform distribution from a = 2 to b = 25. (a) find the probability that x lies between 6 and 11. (b) find the probability that x lies between 11 and 17. (c) find the probability that x lies between 8 and 15. (d) find the probability that x lies between 3 and 22. click the icon to see the definition of the uniform distribution. (a) the probability that x lies between 6 and 11 is 0.217. (round to three decimal places as needed.) (b) the probability that x lies between 11 and 17 is. (round to three decimal places as needed.)

Explanation:

Step1: Recall uniform - distribution formula

For a uniform distribution from $a$ to $b$, the probability density function is $f(x)=\frac{1}{b - a}$ for $a\leq x\leq b$, and the probability $P(c\leq x\leq d)=\frac{d - c}{b - a}$, where $a = 2$ and $b = 25$.

Step2: Calculate probability for part (b)

Substitute $c = 11$, $d = 17$, $a = 2$, and $b = 25$ into the formula $P(c\leq x\leq d)=\frac{d - c}{b - a}$. We get $P(11\leq x\leq 17)=\frac{17 - 11}{25 - 2}=\frac{6}{23}\approx0.261$.

Step3: Calculate probability for part (c)

Substitute $c = 8$, $d = 15$, $a = 2$, and $b = 25$ into the formula. We have $P(8\leq x\leq 15)=\frac{15 - 8}{25 - 2}=\frac{7}{23}\approx0.304$.

Step4: Calculate probability for part (d)

Substitute $c = 3$, $d = 22$, $a = 2$, and $b = 25$ into the formula. We obtain $P(3\leq x\leq 22)=\frac{22 - 3}{25 - 2}=\frac{19}{23}\approx0.826$.

Answer:

(b) $0.261$
(c) $0.304$
(d) $0.826$