The random variable X is uniformly distributed between 70 and 90. The probability of X having a value between 80 and 95 is:

the probability of X having a value between 80 and 95 is 0.5

Step-by-step explanation:

Given that;

random variable x is uniformly distributed

range is 70 to 90

so our first value a is 70 and the second b is 90

Now to find the probability function

substitute the values in the probability density function if the value of x is in between first and second calculated as:

f(x) =  1 / (b - a)

f(x) = 1 / ( 90 - 70)

f(x) = 1 / 20

this means if the value of x is in between the range 70 to 90 then the value of the function is 1/20 and for any other value of x the function is zero

so the probability that x falls between the range of 80 to 95 , p ( 80 ≤ x ≤ 95) is

p = ( b - c ) × f(x)

p = ( 90 - 80 ) × 1/20

p = 10 × 1/20

p = 10/20

p = 0.5

therefore the probability of X having a value between 80 and 95 is 0.5

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."