the normal distribution with mean 68 and standard deviation 16 is a good description of the iowa

Step 1: The event "the student chosen has a score of 3.6 or higher" in terms of X is represented

The normal distribution with mean 68 and standard deviation...

The Normal distribution with mean μμ = 6.8 and standard deviation σσ = 1.6 is a good description of the Iowa Test vocabulary scores of seventh grade students in Gary, Indiana. This is a continuous probability model for the score of a randomly chosen student. Figure 3.1 (p. 68) pictures the density curve. Call the score of a randomly chosen student X for short. Note: If necessary, use <= to represent ≤≤ and >= to represent ≥≥. (a) Write the event "the student chosen has a score of 3.6 or higher" in terms of X. (b) Find the probability of an event which represents "the student chosen has a score of 3.6 or higher".

Transcript

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

00:03 So i'll start by drawing it.

00:04 This is the normal curve.

00:10 The mean, mu, is 6 .8.

00:13 Standard deviation, sigma, is 1 .6.

00:17 And this is for the vocabulary scores of some students.

00:22 We want to find the probability a randomly chosen student has a score of 3 .6 or higher.

00:29 So 3 .6 is below the mean.

00:32 We want that or higher.

00:34 So i'm going to put this as the area to the right, because this is the area corresponding to that probability.

00:42 Pi, what does this look like in terms of x? well, x is the randomly chosen student's score.

00:51 So we want the probability, the x is at least 3 .6.

00:58 How do we find that probability? well, with a normal distribution, we don't really use the raw data.

01:05 We convert it into a z score, and z is equal to x minus mu over sigma.

01:13 So here, we have 3 .6, minus 6 .8, divided by 1 .6, which is minus 2.

01:21 This tells us how many standard deviations away from a mean a value is.

01:26 This one is two standard deviations below the mean.

01:31 Now we need to turn into probability.

01:33 And for that, you need either a z score table, a graph, calculator or something like excel.

01:39 And there are two types of table or two functions that can take you from z score to probability.

01:45 And it really helps to draw this out so you know you're using them correctly.

01:49 You can use either one as long as you use it correctly...

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