A number is selected from a standard normal distribution. What is the probability the number is 0.5000?

Question

 A number is selected from a standard normal distribution. What is the probability the number is 0.5000?

Answer 1

Since the normal distribution (standard or otherwise) is continuous, the probability of an exact value has no meaning and is considered zero.

 

However, some books expect you to interpret P(z = 0.5000) as P(z > 0.5000) = 1 - P(z < 0.5000).  (On a standard normal distribution, mean = 0 and standard deviation = 1.  Therefore, the value is automatically its own z-score).  You can look the probability P(z<0.5000) on a z-score table and use it to calculate the probability P(z > 0.5000).  Hope this helps.