Question

The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400. a. What is the probability of getting more than 12,000 hits?

Answer 1

We have a normal distribution, $\mu=10000, \sigma=2400.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}.\\ \text{a. } z_1=\cfrac{12000-10000}{2400}=0.83;\\ P(X>12000)=P(Z>0.83)=\\ =1-P(Z<0.83)=\\ =1-0.7967=0.2033 \text{ (from z-table)}.\\ \text{b. } z_2=\cfrac{9000-10000}{2400}=-0.42;\\ P(X<9000)=P(Z<-0.42)=\\ =0.3372 \text{ (from z-table)}.$