Final Answer:
The probability (P(z < 1.34)) for a standard normal distribution is approximately 0.9092, rounded to four decimal places.
Step-by-step explanation:
In the context of a standard normal distribution, the variable \(z\) represents the z-score, which measures the number of standard deviations a data point is from the mean. To find \(P(z < 1.34)\), we look up the corresponding area under the standard normal curve to the left of \(z = 1.34\). This can be done using a standard normal distribution table or a statistical software.
Using the standard normal distribution table, we find that the area to the left of (z = 1.34) is approximately 0.9092. This means that the probability that a randomly selected data point from a standard normal distribution is less than 1.34 standard deviations above the mean is approximately 0.9092, expressed as a decimal rounded to four decimal places.
In conclusion, when dealing with standard normal distributions, calculating probabilities involves finding the area under the curve to the left of a specific z-score. In this case, (P(z < 1.34)) signifies the probability that a random data point is less than 1.34 standard deviations above the mean, and the result is approximately 0.9092.