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.
[tex]P(c \leq x \leq d) = \frac{d - c}{b - a}[/tex]
Uniform distribution from a = 4 to b = 29
(a) Find the probability that x lies between 7 and 27.
So [tex]c = 7, d = 27[/tex]
[tex]P(7 \leq x \leq 27) = \frac{27 - 7}{29 - 4} = 0.8[/tex]
80% probability that x lies between 7 and 27.
(b) Find the probability that x lies between 6 and 13.
So [tex]c = 6, d = 13[/tex]
[tex]P(6 \leq x \leq 13) = \frac{13 - 6}{29 - 4} = 0.28[/tex]
28% probability that x lies between 6 and 13.
(c) Find the probability that x lies between 9 and 20.
So [tex]c = 9, d = 20[/tex]
[tex]P(9 \leq x \leq 20) = \frac{20 - 9}{29 - 4} = 0.44[/tex]
44% probability that x lies between 9 and 20.
(d) Find the probability that x lies between 11 and 18.
So [tex]c = 11, d = 18[/tex]
[tex]P(11 \leq x \leq 18) = \frac{18 - 11}{29 - 4} = 0.28[/tex]
28% probability that x lies between 11 and 18.
