To determine the probability of a uniformly distributed random variable, we use the properties of uniform distributions. In this case, the random variable x is uniformly distributed between 70 and 90. This means that every value within this interval has an equal likelihood of occurring.
The total length of the interval where x can take values is:
- Upper Bound: 90
- Lower Bound: 70
- Length of the Interval = Upper Bound – Lower Bound = 90 – 70 = 20
Now, we need to find the probability of x falling between 80 and 95. However, since x can only take values from 70 to 90, we must consider the effective range:
- The lower limit of our specified range is 80.
- The upper limit of our specified range is 90 (as 95 is outside of the interval of x).
Hence, we will calculate the probability for the interval from 80 to 90:
- Length of the Interval = Upper Limit – Lower Limit = 90 – 80 = 10
The probability can then be calculated using the formula for the uniform distribution:
Probability = (Length of Desired Interval) / (Total Length of Interval)
Substituting the values we have:
- Probability = 10 / 20 = 0.5
Therefore, the probability of the random variable x having a value between 80 and 95 (considering the upper limit of 90) is 0.5 or 50%.