the random variable x is known to be uniformly distributed between 70 and 90. the probability of x having a value between 80 to 95 is
so above 90, I assume the distribution is zero, the problem did not state.
range: 70-90 or a range of 20
Pr= 10/20=.5
To find the probability of the random variable x having a value between 80 and 95, we first need to determine the range of x that falls within the given interval.
Given:
Lower bound = 70
Upper bound = 90
We can calculate the range of x within the interval as follows:
Range = Upper bound - Lower bound = 90 - 70 = 20
Since the variable x is uniformly distributed, the probability of x falling within a particular interval is given by the ratio of the interval length to the total range.
Interval length = 95 - 80 = 15
Thus, the probability of x having a value between 80 and 95 can be calculated as:
Probability = Interval length / Range = 15 / 20 = 0.75
Therefore, the probability of x having a value between 80 and 95 is 0.75 or 75%.
To find the probability of a uniformly distributed random variable falling within a specific range, you need to calculate the ratio of the length of the desired range to the total range of possible values.
In this case, the total range of possible values for random variable x is from 70 to 90, which is 20 units (90 - 70).
The desired range is from 80 to 95, which is also 15 units (95 - 80).
To calculate the probability, divide the length of the desired range by the length of the total range:
Probability = Length of desired range / Length of total range
= 15 / 20
= 0.75
Therefore, the probability of x having a value between 80 and 95 is 0.75, or 75%.