Final answer:
To find the value of c for which P(Z < c) = 0.95, we use the calculator command invNorm(0.95, 0, 1) which yields a z-score of approximately 1.645. This indicates c = 1.645. This process is simplified through technology compared to historical methods involving manual lookup in z-tables.
Step-by-step explanation:
To determine the value of c such that P(Z < c) = 0.95, we need to find the z-score that corresponds to the 95th percentile of the standard normal distribution. This is achieved by using a z-table or a calculator with the capability to compute inverse normal probabilities. When using a TI-83, TI-83+, or TI-84+ calculator, we input the command invNorm(0.95, 0, 1) to get the z-score. This command tells the calculator to find the z-score where the area to the left under the standard normal curve is 0.95. As a result, the z-score that we find is approximately 1.645, meaning that c = 1.645. When looking up this value in a z-table, you would find the z-score closest to the area representing 0.95 to the left of the z-value.
Historical Note
The use of technology has made this process much easier than in the past, where one would have to look up values in a z-table. The z-table shows the cumulative probability up to a given z-score, often the area to the left of the designated z-value.