Answer:
P[X>4] = 0.875
Explanation:
Random Variable = X
Mean of variable = 5
Variance of variable = 4/3
Required = Find the probability that X is greater than 4
The variance is a measure of dispersion while the mean is a measure of central tendency.
Variance = 4/3 = 1.333
[5 - 1.333] , [5 + 1.333] = [3.667 , 6.333]
The probability that X>4 is same as the probability that X lies between 4.001 and 6.333
The figure 4.001 is used because X is a continuous variable; it can take on even the most minute values within its range. So if X will be greater than 4, it doesn't have to be 5 or 4.1 ; it can be any value between 4 and 4.1 . For this analysis, 3d.p. (three decimal places) is used, so the next larger number after 4.000 is 4.001 .
6.333 - 3.667 = 2.666
4.000 - 3.667 = 0.333
This makes the probability that X is between the lower limit and 4.000 = 0.333/2.666 = 0.125
6.333 - 4.001 = 2.332
This makes the probability that X is between 4.001 and the upper limit = 2.332/2.666 = 0.875
This is the probability that the continuous random variable X is greater than 4.0
In figures, P[X>4] = 0.875