Final answer:
To find the lower bound of a 0.91 confidence interval, you need to substitute the sample mean, standard deviation, sample size, and the approximated Z-score from the confidence level into the confidence interval formula.
Step-by-step explanation:
To calculate the lower bound of a confidence interval for a given level of confidence, we use the formula:
Lower Confidence Limit = Sample Mean - (Z-score * (Standard Deviation / sqrt(Sample Size)))
In this case, we have a sample mean of 54, standard deviation of 10.8, sample size of 98, and a confidence level of 0.91. First, we need to find the appropriate Z-score for the 0.91 confidence level, which would lie between the Z-scores of the 90% and the 95% confidence intervals given in standard Z-tables.
We approximate this Z-score because exact values for other than common confidence levels like 90%, 95%, or 99% are not typically found in standard tables. Once the Z-score is known, we substitute the values into the formula and solve for the lower limit of the interval.
Calculating the exact lower confidence limit requires access to statistical tables or software to find the precise Z-score.