For two normal distributions with the same mean, but different standard deviations, the 95% confidence interval will be:
(a) The same for both distributions
(b) Larger for the distribution with the smaller standard deviation
(c) Smaller for the distribution with the smaller standard deviation
The standard normal distribution is the normal distribution with a mean of zero and a variance of one. So I would say C
To determine the confidence interval for two normal distributions with the same mean but different standard deviations, we need to understand the concept of the margin of error.
The margin of error is determined by the standard deviation and the desired level of confidence. It represents the range within which the true population mean is likely to fall. A larger standard deviation leads to a larger margin of error, indicating a wider confidence interval. Conversely, a smaller standard deviation results in a smaller margin of error and a narrower confidence interval.
In this case, since the distributions have the same mean but different standard deviations, the confidence interval will be wider for the distribution with the larger standard deviation. This means that the answer is (b) - the 95% confidence interval will be larger for the distribution with the smaller standard deviation.