Final answer:
To find the z-score for an 86% confidence interval, you must look up or interpolate the value that leaves 0.07 in one tail of the standard normal distribution, which would fall between the z-scores for 80% and 90% confidence intervals.
Step-by-step explanation:
The z-score corresponding to an 86% confidence interval cannot be directly read from the standard z-table because most z-tables and calculators provide z-scores for 90%, 95%, and 99.7% confidence intervals as per the empirical rule of 68-95-99.7. However, we can still find the z-score for an 86% confidence interval using statistical software, a calculator, or by interpolating between values from a z-table.
If you have access to a z-table or statistical software, you would look for the area in one tail that corresponds to (1 - 0.86)/2, which is 0.07. You then find the z-score that leaves 0.07 in the tail. According to the empirical rule, known as the 68-95-99.7 rule, the z-score for an 86% confidence interval would be between the z-scores for 80% (which is around 1.28) and 90% (which is around 1.645) confidence intervals. Therefore, you would expect the z-score for an 86% confidence interval to be somewhere between these two values.
When calculating the margin of error (EBM) for a specific confidence level, you would multiply the z-score by the standard deviation and divide by the square root of the sample size if you're estimating a mean. The formula is EBM = za(sigma/sqrt(n)), where Za is the z-score associated with the confidence level, sigma is the population standard deviation, and n is the sample size.