1 Answer

Manotheshark · Answer 1 · 2021-10-19T02:11:09+0000

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.

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.

$P(c \leq x \leq d) = (d - c)/(b - a)$

Uniform distribution from a = 4 to b = 29

(a) Find the probability that x lies between 7 and 27.

So
c = 7, d = 27

$P(7 \leq x \leq 27) = (27 - 7)/(29 - 4) = 0.8$

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

$P(6 \leq x \leq 13) = (13 - 6)/(29 - 4) = 0.28$

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

$P(9 \leq x \leq 20) = (20 - 9)/(29 - 4) = 0.44$

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

$P(11 \leq x \leq 18) = (18 - 11)/(29 - 4) = 0.28$

28% probability that x lies between 11 and 18.

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