Question

If the c.d.f (cumulative distribution function) is given by F(x) = `(x - 25)/10`, then P(27 ≤ x ≤ 33) = ______.

Options

• `3/5`

• `3/10`

• `1/5`

• `1/10`

Answer 1

If the c.d.f (cumulative distribution function) is given by F(x) = `(x - 25)/10`, then P(27 ≤ x ≤ 33) = `underline(3/5)`.

Explanation:

We have,

c.d.f as F(x) = `(x - 25)/10`

∴ P(27 ≤ x ≤ 33) = F(33) - F(27)

`= ((33 - 25)/10) - ((27 - 25)/10)`

`= 8/10 - 2/10 = 6/10 = 3/5`

Second method,

Probability density function f(x) = `"d"/"dx"`(F(x))

`= "d"/"dx" ((x - 25)/10) = 1/10`

∴ P(27 ≤ x ≤ 33) = `int_27^33` f(x) dx

`= int_27^33 (1/10)"dx" = 1/10 int "dx"`

`= 1/10 (33 - 27)`

`= 6/10 = 3/5`