Answer: 0.9772
Step-by-step explanation:
The random variable x is normally distributed with mean[tex](\mu)[/tex] 50 and standard deviation[tex](\sigma)[/tex] 7 .
[tex]P(x>36)=P(\dfrac{X-\mu}{\sigma}>\dfrac{36-50}{7})\\\\=P(Z>\dfrac{-14}{7})\ \ \[Z= \dfrac{X-\mu}{\sigma}]\\\\=P(Z>-2)\\\\=P(Z<2)\ \ \ [P(Z<z)=P(Z>-z)]\\\\= 0.9772\ \ \[\text{By p-value table}][/tex]
Hence, required probability =0.9772
