Suppose x is a uniform random variable with values ranging from 40 to 60. Find the probability that a randomly selected observation exceeds 54. *** Im not sure how to do this. I thought I needed a standard deviation.
To find the probability that a randomly selected observation exceeds 54, you can use the concept of a uniform distribution.
In a uniform distribution, all values within a given range have an equal probability of occurring. In this case, the range of values for the random variable x is from 40 to 60.
First, calculate the total range of values within this range: 60 - 40 = 20.
Next, calculate the range of values that are greater than 54: 60 - 54 = 6.
The probability that a randomly selected observation exceeds 54 is equal to the ratio of the range of values greater than 54 to the total range of values.
So, the probability can be calculated as follows:
Probability = Range of values greater than 54 / Total range of values
= 6 / 20
= 0.3
Therefore, the probability that a randomly selected observation exceeds 54 is 0.3 or 30%.
Note that in a uniform distribution, the standard deviation is not necessary to calculate the probability.