The acme company manufactures widgets the distribution of...

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 35 ounces and a standard deviation of 6 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 95% of the widget weights lie between and b) What percentage of the widget weights lie between 17 and 47 ounces? % c) What percentage of the widget weights lie above 29 ? %

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00:01 So in this question letter a, we should find here, assuming that we have a bell shape, which basically means that we have this, and the middle here is the mean.

00:11 And we can find some points according to what we call the empirical rule.

00:18 So the points that we have is one standard deviation below the mean, so 35 minus 6, which is 23.

00:28 We can find 35 minus, oh, sorry.

00:31 This is 2.

00:32 Let me add another one, and another one.

00:35 So we have 3.

00:37 So for example, the first one is, like i said, is like 35 minus 6, which is 29.

00:44 Then we have, if you subtract another 6, you have 23.

00:48 And if you subtract another 6, you have 17.

00:51 And if you do the same thing for the other side, you have 41, then 47, and then 53.

01:00 So now what we have, because we have the bell shape, is that the area that we have here, which is within one standard deviation, is 68 % of the observations.

01:11 We have here 95, and we have here 99.

01:17 So in the first part of this question, you're interested in the 95%.

01:21 So using the empirical rule, we know that the values will be between 23 and 47.

01:28 So we don't need to do any other calculation.

01:30 Then for letter b, we are interested in the percentage of values that are between 17, so this value, and 47, which is this...

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