Scores on a common final exam in a large enrollment multiple...

Scores on a common final exam in a large enrollment, multiple-section freshman course are normally distributed with mean 72.7 and standard error of 1.31 for a sample of 100. Calculate the minimum score that need to be scored by a student for the probability to exceed 95% of marks.

Transcript

00:01 All right.

00:02 So we have a file exam in a big freshman course and the scores are normally distributed with this given mean 72 .7 and a standard error of 1 .13 with a big sample size.

00:16 That's nice because we can be assured that's normally distributed.

00:22 So we want to find the minimum score that needs to be scored for a student by a student for the probability to exceed 95 % of the marks, basically in the top 95 % of the mark.

00:41 So we could use we're going to use the z score, but i'm going to tell you what the value is and i have a nice formula so it's norm .in.

00:48 What you do is you put the percentage you want 0 .95 with the mean 72 .7 and the standard deviation 1 .31 and that's the score you would need and if you're if your professor wants you to do the lookup table, you'd still get this value.

01:08 What you would do is you go go to a lookup table you'd find the probability that would be 0 .95 and you'd actually give a z score of roughly 1 .644 and then you would use this value that's your z then solve for x and and then do that there but so let's see it'd be one but you took up the same thing as what i just got there 644 that's the z then we're going to multiply by a standard error 1 .31 and then we're going to add the mean to it because they're going to undo this a little bit here so add 72 .7 and we're getting roughly that same thing i mean we approximated here with that z score of 1 .644 but you can see they're kind of the same and you know maybe this is a pretty tight range 1 .3 that's a pretty pretty narrow range for some of the the data, let's say it was, i don't know, 13 .1.

02:14 Then you would just change this to be 13 .1 for the standard deviation...

Question

Scores on a common final exam in a large enrollment, multiple-section freshman course are normally distributed with mean 72.7 and standard error of 1.31 for a sample of 100. Calculate the minimum score that need to be scored by a student for the probability to exceed 95% of marks.

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