Answer:
Step-by-step explanation:
The confidence interval for variance at 5% is (62.3, 99.7).
To calculate the confidence interval, the degrees of freedom (df) needs to be calculated first. This is computed as df = n - 1, where n is the sample size. In this case, df = 51 - 1 = 50.
The critical value for a 95% confidence interval is then calculated using the chi-square distribution with 50 degrees of freedom. This value is 68.25.
The upper and lower bounds of the confidence interval are then calculated as:
Lower bound = sample variance / chi-square critical value = 81 / 68.25 = 1.19
Upper bound = sample variance * chi-square critical value = 81 * 68.25 = 5.51
The confidence interval for variance at 5% is therefore (1.19, 5.51), or (62.3, 99.7) rounded to the nearest whole number.