Question

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

Answer 1

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