Consider P(X >10)=0.9983 where it is given that Xis distributed toN (mean ;25). Determine mean
Given that P(X > 10) = 0.9983, we can find the z-score corresponding to this probability:
P(Z > ((10 - mean) / standard deviation)) = 0.9983
Using a Z-table, we find that the z-score corresponding to a probability of 0.9983 is approximately 2.57.
Now, we know that the mean is 25 and the standard deviation is the square root of the variance, which is given by the formula:
Var(X) = σ^2 = 25
Solving for the standard deviation, we get:
σ = √25 = 5
Now we can use the z-score formula to find the value of the mean:
2.57 = (10 - 25) / 5
2.57 = -3
-3 = 10 - mean
mean = 10 + 3
mean = 13
Therefore, the mean of the distribution is 13.