Question

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 is 0.0378

Explanation:

Given that;

cumulative distribution function: F (x ) = 1 - ( 1 / ( x + 1)³ )

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

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

p( 0.9 < x < 0.9 ) = [1 - ( 1 / ( 1.1 + 1)³ )] - [1 - ( 1 / ( 0.9 + 1)³ )]

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

= [1 - 0.107979] - [1 - 0.14579]

= 0.8920 - 0.8542

= 0.0378

Therefore, the probability is 0.0378