Question

The time it takes to preform a task has a continuous uniform distribution between 43 min and 57 min. What is the the probability it takes between 52.3 and 54.7 min. Round to 4 decimal places.

Answer 1

The values is
`P(52.3 < X < 54.7 ) = 0.17142`

Explanation:

From the question we are told that

The lower limit of the interval is a = 43 minutes

The upper limit of the interval is b = 57 minutes

Generally the probability distribution function of uniform distribution is mathematically represented as

`F(x) = \left \{ { a, b \atop {0 } \ \ \ \ \ \ otherwise} \right.`

Generally the probability it takes between 52.3 and 54.7 min is mathematically represented as

`P(52.3 < X < 54.7 ) = \int\limits^(52.4)_(54.7) {F(x)} \, dx`

=>
`P(52.3 < X < 54.7 ) = \int\limits^(52.4)_(54.7) {(1)/(57- 43) } \, dx`

=>
`P(52.3 < X < 54.7 ) = \int\limits^(52.4)_(54.7) {(1)/(14) } \, dx`

=>
`P(52.3 < X < 54.7 ) = {(1)/(14) } \int\limits^(52.4)_(54.7) \, dx`

=>
`P(52.3 < X < 54.7 ) = {(1)/(14) } [x] \ | \left 54.7} \atop {52.3}} \right.`

=>
`P(52.3 < X < 54.7 ) = (54.7 -52.3)/(14)`

=>
`P(52.3 < X < 54.7 ) = 0.17142`