The z-score is defined as follows:
Where x is the observed mean, is the population mean, and is the standard deviation. The z number converts the given values into standard units based on the standard deviation. Consider the first question. What is our z-score? The difference of the observed is 8 greater than the mean (= 48 - 40). Thus, the observed mean is one standard deviation from the mean. One thing you should know is that 68% of the population is within one standard deviation of the mean. This means that 100% less 68% (= 32%) of the observations fall outside of one standard deviation from the mean. But we're not concerned with just all observations. We're concerned with those on the positive side: i.e., for those observations . Since the normal distribution is symmetric, there is an equal number on both sides of one standard deviation from the mean. Therefore, we only need to consider half. Therefore, 16 (= 32/2) percent of the observations lie positively one standard deviation from the mean. In other words, you have a 16% chance of being observed given this normal distribution.
Did you understand that? The second question is just a calculation. Interpret it correctly: how many standard deviations is 1600 from the mean of 1000 when ?