The waiting time for a bus has a uniform distribution between 2 and 13 minutes. What is the probability that the waiting time for this bus is less than 4.5 minutes on a given day

0.2273

Step-by-step explanation:

Probability density function for uniform distribution is given by :-

, where x is uniformly distributed in [a,b].

Let x denotes the waiting time for this bus.

Given : The waiting time for a bus has a uniform distribution between 2 and 13 minutes.

Probability distribution function of x for interval [2,13] will be :-

Required probability : P(x<4.5) =

Hence, the probability that the waiting time for this bus is less than 4.5 minutes on a given day = 0.2273

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is