Z-Score +Table Usage

Question

Given average cost of 200, and standard deviation of 50, what is the probability that the individual will pay at least 300? I got the Z-score as 2 but now I'm wondering is the probability 0.977 or am I missing something.

Answer 1

Comment continued. For such problems, it's always a good idea to try making a sketch. Here is a sketch for the original problem in R:

curve(dnorm(x,200,50), 50, 350, ylab="PDF", main="NORM(200,50)")
 abline(h=0, col="green2")
 abline(v=300, col="red")
 abline(v=c(150,250), col="green2", lty="dotted")

Of course, your freehand sketch will not be a precise as you'd get from software, but you can get a good enough graph to avoid gross errors. [It helps to know that the inflection points, between convex in the center and concave in the tails, occur at $\mu\pm\sigma;$ here that's $200\pm 50$ or 150 & 250. Areas outside of inflection points are about 16% on either side.]