One/Two tailed confidence interval of a single random variable in case of unknown mean and known variance

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Suppose we have a random variable $Y$ which follows normal distribution of unknown mean $\mu$ and variance is $9$. Suppose we have to calculate the one or two tailed confidence interval, will the formula be the same i.e.
$ P( -z_{\alpha/2} \le \frac{Y - \mu}{\sigma} \le z_{\alpha/2})$