A bank's loan officer rates applicants for credit. The...

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If 36 different applicants are randomly selected, find the probability that their mean is: a) below 220 A) 0.6782 B) 0.9918 C) 0.8349 D) 0.7231 b) above 215 A) 0.9641 B) 0.8178 C) 0.0359 D) 0.1822

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 We're looking at a normal distribution.

00:02 Its mean is 200, its standard deviation is 50.

00:07 But we are not looking at individual applicants.

00:10 We are looking at a sample of size 36.

00:13 So we want to look at probabilities for the sample mean.

00:17 How does taking a sample influence things? well i'm going to refer to the central limit theorem, which states that as sample size increases, sample means become more and more normally distributed compared to the population.

00:31 Here we are starting with a normal population.

00:33 You can't get more normal than normal.

00:35 So if i took every sample of this size, took the means, plotted them out, i just get another normal curve.

00:42 The mean of the means is the same as the population mean.

00:46 The standard deviation of the sample means, or standard error, is sigma over root n.

00:51 So 50 over root 36 is 50 over 6, which i will just leave like that.

00:59 So in part a, what is the probability their mean is below 220? so that's above the mean, i'll mark it on here.

01:09 We want below that, so this area to the left.

01:13 At this point i need something with the normal distribution built into it.

01:17 That could be software like excel or r.

01:19 I'm going to use my ti -84 calculator with the normal cdf function...

Question

Please give Ace some feedback