Question

(Hypothetical.) Suppose a certain person's reaction time, in seconds, for pressing a button on a visual cue has the following cumulative distribution function: F (x )equals 1 minus fraction numerator 1 over denominator (x plus 1 )cubed end fraction space x greater than 0 What is the probability the person's reaction time will be between 0.9 and 1.1 seconds

Answer 1

the probability the person's reaction time will be between 0.9 and 1.1 seconds is 0.0378

Step-by-step explanation:

Given the data in the question;

the cumulative distribution function F(x) =
`1 - (1)/((x + 1)^3)` ;
`x > \theta`

probability the person's reaction time will be between 0.9 and 1.1 seconds

P( 0.9 < x < 1.1 ) = P( x ≤ 1.1 ) - P( x ≤ 0.9 )

P( 0.9 < x < 1.1 ) = F(1.1) - F(0.9)

= [
`1 - (1)/((x + 1)^3)` ] - [
`1 - (1)/((x + 1)^3)` ]

we substitute

= [
`1 - (1)/((1.1 + 1)^3)` ] - [
`1 - (1)/((0.9 + 1)^3)` ]

= [
`1 - (1)/((2.1)^3)` ] - [
`1 - (1)/((1.9)^3)` ]

= [
`1 - (1)/((9.261))` ] - [
`1 - (1)/((6.859))` ]

= [ 1 - 0.1079796998 ] - [ 1 - 0.1457938 ]

= 0.8920203 - 0.8542062

= 0.0378

Therefore, the probability the person's reaction time will be between 0.9 and 1.1 seconds is 0.0378