Answer: 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
