Essentials of Statistics (5th Edition)

Although the dot plot is not roughly bell-shaped, the sample size is more than 30 (it is 40), hence the sample data is roughly normally distributed, hence $\alpha=1-0.99=0.01.$ $\sigma$ is known, hence we use the z-distribution with the table. $z_{\alpha/2}=z_{0.05}=2.575.$