The table containing the mean, variance is shown below.
The mean is 65.
Use the equation to find the variance.
Use the equation to find the standard deviation.
The t value corresponding to confidence interval is 2.26.
Use the equation to construct the confidence interval.
Therefore, the upper and lower limits are and
Given that, the variance of the distribution is 25.
Use the equation to construct the interval.
The upper and lower limits of the confidence interval is and
The standard deviation is defined as the degree of variance of value from mean value.
In part (b) the standard deviation is higher compared to part (a).
Therefore, the deviation is higher. So, the confidence interval got widened.