Question

Consider a uniform distribution from aequals4 to bequals29. ​(a) Find the probability that x lies between 7 and 27. ​(b) Find the probability that x lies between 6 and 13. ​(c) Find the probability that x lies between 9 and 20. ​(d) Find the probability that x lies between 11 and 18.

Answer 1

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.