Final answer:
To find the probability P(z < 1.16), look it up directly in a z-table, which provides the cumulative area to the left of a z-score. The probability P(z < 1.16) for a standard normal distribution is 0.8770 when rounded to four decimal places.
Step-by-step explanation:
To find the probability P(z < 1.16) for a standard normal distribution, you would typically use a z-table, calculator, or statistical software. Since most z-tables provide the area to the left of a z-score, you can directly find the probability by looking up the z-score of 1.16. If the z-table shows the area to the left of z is 0.8770, that means P(z < 1.16) is 0.8770. This value expresses the cumulative probability from the far left of the distribution up to a z-score of 1.16.
In case the z-table you're using does not directly give the area for z = 1.16, you may need to interpolate between the closest tabulated values. For the given task, no interpolation is necessary as we can use the known value. Therefore, the sought probability, rounded to four decimal places, is 0.8770.