Answer:
a) 80% probability that x lies between 7 and 27.
b) 28% probability that x lies between 6 and 13.
c) 44% probability that x lies between 9 and 20.
d) 28% probability that x lies between 11 and 18.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value x between c and d, in which d is larger than c, is given by the following formula.
![P(c \leq x \leq d) = \frac{d - c}{b - a}](https://tex.z-dn.net/?f=P%28c%20%5Cleq%20x%20%5Cleq%20d%29%20%3D%20%5Cfrac%7Bd%20-%20c%7D%7Bb%20-%20a%7D)
Uniform distribution from a = 4 to b = 29
(a) Find the probability that x lies between 7 and 27.
So ![c = 7, d = 27](https://tex.z-dn.net/?f=c%20%3D%207%2C%20d%20%3D%2027)
![P(7 \leq x \leq 27) = \frac{27 - 7}{29 - 4} = 0.8](https://tex.z-dn.net/?f=P%287%20%5Cleq%20x%20%5Cleq%2027%29%20%3D%20%5Cfrac%7B27%20-%207%7D%7B29%20-%204%7D%20%3D%200.8)
80% probability that x lies between 7 and 27.
(b) Find the probability that x lies between 6 and 13.
So ![c = 6, d = 13](https://tex.z-dn.net/?f=c%20%3D%206%2C%20d%20%3D%2013)
![P(6 \leq x \leq 13) = \frac{13 - 6}{29 - 4} = 0.28](https://tex.z-dn.net/?f=P%286%20%5Cleq%20x%20%5Cleq%2013%29%20%3D%20%5Cfrac%7B13%20-%206%7D%7B29%20-%204%7D%20%3D%200.28)
28% probability that x lies between 6 and 13.
(c) Find the probability that x lies between 9 and 20.
So ![c = 9, d = 20](https://tex.z-dn.net/?f=c%20%3D%209%2C%20d%20%3D%2020)
![P(9 \leq x \leq 20) = \frac{20 - 9}{29 - 4} = 0.44](https://tex.z-dn.net/?f=P%289%20%5Cleq%20x%20%5Cleq%2020%29%20%3D%20%5Cfrac%7B20%20-%209%7D%7B29%20-%204%7D%20%3D%200.44)
44% probability that x lies between 9 and 20.
(d) Find the probability that x lies between 11 and 18.
So ![c = 11, d = 18](https://tex.z-dn.net/?f=c%20%3D%2011%2C%20d%20%3D%2018)
![P(11 \leq x \leq 18) = \frac{18 - 11}{29 - 4} = 0.28](https://tex.z-dn.net/?f=P%2811%20%5Cleq%20x%20%5Cleq%2018%29%20%3D%20%5Cfrac%7B18%20-%2011%7D%7B29%20-%204%7D%20%3D%200.28)
28% probability that x lies between 11 and 18.