A sample of n = 25 observations is drawn from a normal population with ų =1000 and ó = 200 . Find p( X > 1100)
To find P(X > 1100), we first need to calculate the z-score for 1100 using the formula:
z = (X - ų) / σ
z = (1100 - 1000) / 200
z = 100 / 200
z = 0.5
Next, we need to look up the corresponding probability for this z-score in the standard normal distribution table. The table gives us that P(Z < 0.5) = 0.6915.
Since the normal distribution is symmetric, P(Z > 0.5) = 1 - P(Z < 0.5) = 1 - 0.6915 = 0.3085.
Therefore, P(X > 1100) = 0.3085 or 30.85%.