A professor at a local university noted that the grades of...

A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 10. a. The professor has informed us that 16.6 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? (8 points) b. If 12.1 percent of her students failed the course and received F's, what was the maximum score among those who received an F? (8 points)

Transcript

00:01 All right, in your question, you're told a professor at a local university noted that grades of our students were normally distributed with a mean of 78 and a standard deviation of 10.

00:10 In part a, you're told, the professor told you that 16 .6 % of the students received grades of a, and we're trying to figure out what is the minimum score for a grade of a.

00:22 So i'm going to start by drawing a normal model.

00:25 You were told that the grades are normally distributed, and we have a mean of a minimum.

00:34 78 and we're trying to find this score up here somewhere i'm going to call x such that that the area to the right of that is 16 .6 percent.

00:46 Now we want to think of that as a decimal 1 .66 and now i'm going to use a z table to try to find the z score for that position.

00:57 Now a z and we get 0 .834.

01:11 Looking at a positive z table, i'm searching through the field.

01:16 I'm searching through the field everywhere, looking, looking, looking for 0 .834.

01:23 So 0 .834.

01:25 I'm getting closer.

01:26 Getting closer.

01:29 Right there it is exactly.

01:31 And that works out to be 0 .9.

01:35 I'll highlight 0 .9.

01:40 7 .97.

01:42 Okay, so i'm going to bring that back to my work.

01:45 The z score is .97.

01:50 Now the formula for a z score is to take the data value, which we'll call x, minus the mean divided by standard deviation.

02:01 We now know that our z score is .97...

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