Final Answer:
The probability P(z < 2.15) for a standard normal distribution is approximately 0.9842 when rounded to four decimal places.
Step-by-step explanation:
In a standard normal distribution, the area under the curve to the left of a specific z-value represents the cumulative probability up to that point. Using a z-table or statistical software, we find that the z-score of 2.15 corresponds to an area or probability of approximately 0.9842.
This means that there's a 98.42% probability of observing a value less than 2.15 standard deviations above the mean in a standard normal distribution. Visualizing this on a standard normal curve, the shaded area to the left of the z-score 2.15 represents this probability.
Understanding probabilities in a standard normal distribution is crucial in various fields, especially in statistics, where it helps in making predictions or drawing conclusions about certain events or values based on their likelihood within a standard normal curve.