Boo boo b gone is the brand of an antiseptic solution...

“Boo Boo B Gone” is the brand of an antiseptic solution manufactured by MedAid. The company uses a high-speed machine to fill its small plastic bottles for distribution. The amount of liquid dispensed by the machine into the bottles forms a normal distribution. A random sample of 12 jars is taken from the production line and tested by quality control. The sample is found to have a mean of 93.50 mL and a standard deviation of 7.38 mL. Using this sample, calculate the upper limit of a 90% confidence interval for the amount of liquid dispensed into the bottles. Round your answer to 2 decimal places.

Transcript

00:01 Okay, for your question, you're told that a random sample of 12 jars has been taken from the production line and tested by quality control.

00:09 The sample was found to have a mean of 93 .50 milliliters, and you were told that the standard deviation for the sample is 7 .38 milliliters.

00:26 Now, there's a couple important pieces of information here before i move forward.

00:30 You are told that the amount of liquid dispensed by the machine into the bottles forms a normal distribution.

00:39 That is very crucial that we were told that it was a normal distribution for when we find the critical value.

00:48 Because since we know that the population is a normal distribution, we are allowed to use a z critical value.

00:59 If we would have not known that it was a normal distribution, we would have had to use a t critical value and work with something called degrees of freedom.

01:10 You can avoid degrees of freedom if your sample size is large enough.

01:15 The boundary is usually 30, and ours is well below 30.

01:19 So if i wouldn't have been told normal distribution, i would be looking for a t.

01:25 But since we were told, i'll be looking for a z.

01:27 And we'll get into that here in a minute.

01:29 Then i'll be looking for a z using a z table for the critical value.

01:34 Your question is to find the upper limit of a 90 % confidence interval.

01:40 So let's draw out what that actually means.

01:49 So we have our normal distribution and your x bar, your mean is going to be in the center of that, 93 .50.

01:58 And we want to block off the middle 90 % of data.

02:06 We want to find out what the amount of milliliters would be here, potentially, although your question only wants the high limit.

02:16 We could find either with our confidence interval.