Use the Empirical Rule. The monthly utility bills for eight...

Use the Empirical Rule. The monthly utility bills for eight more households are listed. Using the sample statistics from Exercise $30,$ determine which of the data entries are unusual. Are any of the data entries very unusual? Explain your reasoning. $\$ 65, \$ 52, \$ 63, \$ 83, \$ 77, \$ 98, \$ 84, \$ 70$

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00:01 Hey there, welcome to numerate.

00:03 So we're looking at the monthly utility bills here, where it basically looks at the dollar amount per month, right? so which of these data entries are very unusual here? based on the exercise 30 mean and standard deviation values that are given.

00:24 So what are the very unusual data entries? so very unusual equals basically values that are greater than three z scores away.

00:45 Or it can be negative z scores as well, right? so let's write down what we're given.

00:50 So we're given a mean of around, let's see here.

00:56 65, 52, 70.

00:59 So our mean here is, the mean monthly chili bill is 70.

01:05 And the standard deviation is 8.

01:09 So we have 8 as our standard deviation and 70 as our mean.

01:16 So with this, we're going to use the z score equation here.

01:20 Z equals x value minus the mean divided by the standard deviation.

01:27 So we're going to look at the lowest value and highest value to find which z score here is the lowest.

01:37 I mean, just these scores that are very unusual.

01:40 So it's lowest.

01:42 Lower than 3, lower than negative 3, and higher than positive 3.

01:47 So with this, let's find the lowest.

01:51 First, so it looks like our lowest here is 52.

01:55 So let's try 52...

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