Statistics normal distribution

Question

The weekly amount of money spent on maintenance and repairs by a company was observed,
over a long period of time, to be approximately normally distributed with mean $400 and standard
deviation $20. If $450 is budgeted for next week, what is the probability that the actual costs will
exceed the budgeted amount?

 

Solution: P(Y > 450) 
             = P(Z > 2.5)
             = 0.0062

 

I dont understand why its not 0.5-0.0062=0.4938 ? Ive been watching a ton of videos on youtube and that is the approach they have been using but in various solution manuals it shows just looking up the z value in the table and nothing about subtracting 0.5. Im so confused !!

Answer 1

.4938 is the probability that z lies between the mean and 2.5 standard deviations from the mean; your problem wants the probability that z is greater than 2.5 standard deviations from the mean, which is .5-.4938.

Remember that a distribution function gives the probability of a variable being LESS than a given value.

The tables for the standard normal only print the values for deviations greater than the mean, so the total probability for a variable greater than the mean is .5.