A large manufacturing firm tests job applicants test scores...

A large manufacturing firm tests job applicants. Test scores are normally distributed with a mean of 500 and a standard deviation of 50. Management is considering placing a new hire in an upper-level management position if the person scores in the upper sixth percent of the distribution. What is the lowest score a new hire must earn to qualify for a responsible position?

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Transcript

00:01 Hello everyone and welcome.

00:03 This is a question regarding statistics and we want to see what the lowest score a new hire must earn in order to qualify for a position that is normally distributed with the mean of 500 and a standard deviation of 50.

00:18 And he has to be in the upper 6 % of the distribution.

00:24 So yeah, there's a lot of statistics involved in this question.

00:27 The first thing we have to do is make our normal model.

00:30 So we have x.

00:31 And remodeling it with a normal model, normal distribution, where the mean is 500, and the standard deviation is 50.

00:48 Right, so this was all given to us in the question itself.

00:53 And then we now we have to find the critical value.

00:56 And we're already to find the critical value in our standard normal table, we first have to see what probability we're looking at.

01:04 Because you see if this is our curve right over here, then 6 % is something like here.

01:11 We want all of this stuff.

01:13 So this is going to be 1 minus 0 .06, which is 94%.

01:18 So 0 .94.