The number of credits taken by college students is...

The number of credits taken by college students is approximately Normally distributed with mean 15 units and standard deviation 3.1 units. Round your answers to 4 decimal places. What is the probability that a college student selected at random is taking between 14 and 16 credits? P(14 < x < 16) = 0.2530 If a random sample of 8 college students is selected, what is the probability that the mean number of credits they are taking is between 14 and 16? P(14 < \bar{x} < 16) =

Transcript

00:01 So in this problem we're told that a counselor that's new to a college was told that the average credit students register for each semester is 12 .4 with a standard deviation of 1 .8 credits.

00:11 Let's jot that down.

00:13 Our mean is 12 .4 and our standard deviation is 1 .8.

00:18 It says the counselor takes a random sample of 40 students and collects the number of credits that they register.

00:23 So our sample size here is 40.

00:26 And we're asked to first find the mean and the standard deviation of the sampling distribution.

00:31 So the mean of the sampling distribution is equal to the population mean, which we were told is 12 .4.

00:38 So there's no more calculating to be done there.

00:42 But the standard deviation for the sampling distribution is equal to the population standard deviation divided by the square root of the sample size n.

00:50 So for this we'll have to do a little bit more calculating.

00:53 But it's not too bad because all we have to do is divide our population standard deviation, 1 .8, by the square root of our sample size n, which is 40.

01:03 Now when we calculate that, we're onto two decimal places, we get 0 .28 as our standard deviation for the sample.

01:10 Now that we have those two values, we're asked to find the probability that within this sample of 40 students the average credits registered will be more than 13...

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