Step 1 :Given values are mean = 121, standard deviation = 19, sample size = 90, and z-score for 99% confidence interval = 2.576.
Step 2 :First, calculate the margin of error using the formula: \( z \times \frac{standard deviation}{\sqrt{sample size}} \).
Step 3 :Substitute the given values into the formula to get: \( 2.576 \times \frac{19}{\sqrt{90}} \approx 5.159 \).
Step 4 :Next, calculate the lower and upper limits of the confidence interval using the formulas: \( mean - margin of error \) and \( mean + margin of error \) respectively.
Step 5 :Substitute the values into the formulas to get: \( 121 - 5.159 \approx 115.8 \) and \( 121 + 5.159 \approx 126.2 \).
Step 6 :Round the lower and upper limits to one decimal place to get: lower limit = 115.8 and upper limit = 126.2.
Step 7 :Final Answer: The lower limit of the 99% confidence interval for the true mean hourly fee of all consultants in the industry is \( \boxed{115.8} \) and the upper limit is \( \boxed{126.2} \).