In this paper, we show that the generalized Aluthge transformations of a large class of operators (weighted conditional type operators) are normal. As a consequence, the operator $M_wEM_u$ is $p$-hyponormal if and only if it is normal, and under a weak condition, if $M_wEM_u$ is normal, then the Holder inequality turn into equality for $w$, $u$. Also, we give some applications of $p$-hyponormal weighted conditional type operators, for instance, point spectrum and joint point spectrum of $p$-hyponormal weighted conditional type operators are equal. In the end, some examples are provided to illustrate concrete application of the main results of the paper.