Final answer:
To determine the value of X in a standard normal distribution, identify the target probability, then use a z-table, calculator, or invnorm function to find the corresponding z-score.
Step-by-step explanation:
To find the value of X for a standard normal distribution (where X follows N(0,1)), we use a z-table or similar tools like calculators with statistical functions. The first step is to determine the desired probability or percentile that corresponds to our target X value. Once the probability is known, we can use the table, calculator, or invnorm function to find the z-score that has the cumulative area to the left of it equal to the probability.
For example, if we want to find the X value that falls at the 97.5th percentile, we use invnorm(0.975,0,1) to get the z-score. Then, we would look up this z-score in the z-table, under the z-column, which will correspond to the 97.5th percentile, to find the X value. Remember, a standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1.
Note: If X follows a normal distribution with a different mean (μ) or standard deviation (σ), you will have to standardize the value by subtracting the mean from X and dividing by the standard deviation before looking it up in the z-table.