Question

Assume the random variable x is normally distributed with mean 50 and standard deviation 7 . Find the indicated probability. P(X>36)

Answer 1

Answer: 0.9772

Step-by-step explanation:

The random variable x is normally distributed with mean$(\mu)$ 50 and standard deviation$(\sigma)$ 7 .

$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}]$

Hence, required probability =0.9772