What is the probability that x will equal 23?

Question

x is the number of emails at a certain email address on any randomly selected day. It is approximately normally distributed, with a mean of 18 and a standard deviation of 6. What is the probability that x will equal 23?

Answer 1

The normal distribution deals with continuous probability, so to accommodate a discrete value we need to calculate the probabilities for 22.5 and 23.5 and then subtract. We need two Z scores:

Z1=(22.5-18)/6=4.5/6=0.75 and Z2=(23.5-18)/6=5.5/6=0.9167.

p(Z1)=0.7734, p(Z2)=0.8203. Therefore p(X=23)=0.8203-0.7734=0.0469 or 4.69% approx.

Comments

Hello Rod, thank you for your help as always.