Answer:
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) = [tex]1 - \frac{1}{(x + 1)^3}[/tex] ; [tex]x > \theta[/tex]
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)
= [ [tex]1 - \frac{1}{(x + 1)^3}[/tex] ] - [[tex]1 - \frac{1}{(x + 1)^3}[/tex] ]
we substitute
= [ [tex]1 - \frac{1}{(1.1 + 1)^3}[/tex] ] - [[tex]1 - \frac{1}{(0.9 + 1)^3}[/tex] ]
= [ [tex]1 - \frac{1}{(2.1)^3}[/tex] ] - [[tex]1 - \frac{1}{(1.9)^3}[/tex] ]
= [ [tex]1 - \frac{1}{(9.261)}[/tex] ] - [[tex]1 - \frac{1}{(6.859)}[/tex] ]
= [ 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
