Final answer:
To find P( z < 1.60 or z > 2.50) in a standard normal distribution with mean 0 and standard deviation 1, one must calculate the areas to the left and right of the given z-scores using a Z-table and combine them to get the total probability.
Step-by-step explanation:
The student is asking about finding the probability for a z-score outside two specified points in a standard normal distribution, which has a mean of 0 and a standard deviation of 1. The standard normal distribution is denoted as Z ~ N(0, 1). To answer this, we use a Z-table or statistical software to find the area to the left of z = 1.60 and the area to the right of z = 2.50. We then subtract each from 1 to get their respective tails and add them together to get the total probability.
The probability of z < 1.60 is found by looking up the value in the Z-table, which gives us the cumulative area to the left. The remainder, 1 minus this cumulative area, gives us the probability for z > 1.60. Similarly, for z > 2.50, we find the cumulative area to the right from the Z-table. Finally, since the events are disjoint (they cannot happen at the same time), we add these two probabilities together to find P( z < 1.60 or z > 2.50).