Final Answer:
The value of z for 0.755 is approximately 0.2266 (Option 1).
Step-by-step explanation:
To find z for 0.755, we need to refer to a standard normal distribution table or use a calculator. The given value 0.755 represents the area under the standard normal distribution curve up to z. By consulting a z-table or using a calculator, we can find the corresponding z-score. The z-score is the number of standard deviations a data point is from the mean in a normal distribution.
The calculation involves finding the inverse of the cumulative distribution function (CDF) for the standard normal distribution. This can be done using statistical software, a calculator, or a z-table. The resulting z-score for 0.755 is approximately 0.2266.
In conclusion, Option 1 (0.2266) is the correct answer, representing the z-score for the given cumulative probability of 0.755. This process is fundamental in statistics and is used to analyze and interpret data in various fields.