finding the estimated area to the right side of a normal curve

Question

karla tutors statistics during her summer vacation. the random variable T represents how much money she makes. assume T is normal and has a mean of $240 and a standard deviation of $60 . There is an approximately .6 probability that, in a randomly selected summer break, karla will make less than about

Answer 1

Based on the fact that we are only on the right side of the bell curve and .6 is taken off, this leaves .44. If we look at a z-table, we see that .44 corresponds to a Z score of 1.56. Let's use the scenario information to solve for T. For our purposes, I will use T instead of x as the amount of money Karla makes.

The Z formula is: Z = T - Mean

SD

So, using Algebra we have to move the standard deviation (SD) amount of $60 to the other side where Z is located. This would leave us with 1.56 x 60 = 93.6

Now add $93.60 to $240 and we get $333.60

Translation: There is a .6 probability that Karla will make less than 333.60