if the mean=100 and the standard deviation=8,
calculate
p(x>108)
To calculate the probability of x being greater than 108, we can use the Z-score formula.
The Z-score formula is given by:
Z = (X - μ) / σ
Where:
Z is the standard score (Z-score)
X is the value we want to find the probability for (108 in this case)
μ is the mean (100 in this case)
σ is the standard deviation (8 in this case)
First, let's calculate the Z-score for x = 108 using the formula:
Z = (108 - 100) / 8 = 8 / 8 = 1
Next, we need to find the probability corresponding to this Z-score using a Z-table or a statistical calculator. The Z-table provides the cumulative probability up to a given Z-score. Since we are interested in finding the probability of x being greater than 108, we need to find the area under the normal curve beyond the Z-score of 1.
Looking up the Z-table, we find that the probability of Z being less than or equal to 1 is approximately 0.8413. Therefore, the probability of Z being greater than 1 is equal to 1 - 0.8413 = 0.1587.
So, the probability of x being greater than 108 is approximately 0.1587 or 15.87%.