Question

Hey guys, I really need help! Will fan and medal :)

Scores on a statewide standardized test are normally distributed with a mean of 12.89 and a standard deviation of 1.95. Certificates are given to students whose scores are in the top 2% of those who took the test. This means that they scored better than 98% of the other test takers. Marcus received his score of 13.7 on the exam and is wondering why he didn’t receive a certificate. Show all work to determine whether Marcus’ score was high enough to earn a certificate. Write Marcus a letter about why he didn't recieve a certificate.

Answer 1

Oh, and include a brief summary of your statistical analysis in your letter. :) Almost forgot.

Answer 2

his score is 13.7, the mean is 12.89, and the standard deviation is 1.95

convert his score to a z-score using the formula z-score = (given value - mean)/standard deviation

then, use your calculator to determine the percentage of data values that fall below mark's score (normalcdf(-99, marks score)). if this value is greater than 0.98, then that means that Mark is in the top 2%. Otherwise, Mark is not in the top 2%.

Answer 3

small correction:

normalcdf(-99, marks z-score)

Answer 4

So the z-score would be 13.7 - 12.89/1.95?

Answer 5

parentheses

Answer 6

So (13.7 - 12.89)/1.95?

Answer 7

yes

Answer 8

Now, I'm kind of confused about finding the marks below Marcus' score...

Answer 9

normalcdf(-99, marcus' z-score)

I meant to say "Marcus", not "Mark")

Answer 10

Sorry, the data points below Marcus' score

Answer 11

what is normalcdf(-99, marcus' z-score)?

Answer 12

What does normalcdf mean?

Answer 13

do you know how to use a graphing calculator?

Answer 14

Umm, no... But I have a regular scientific one

Answer 15

I don't need one for what I'm doing... Maybe... I'm not sure lol :P

Answer 16

hm, did your teacher show you how to use a z-table?

Answer 17

Yes :) I have a z-table for positive and negative values.

Answer 18

great!

Marcus' z-score is 0.415, do you know how to use the z-table to find the area to the left of the z-score?

Answer 19

I think so. Is it .65910?

Answer 20

yup, that's about what I got, too!

do you know what .65910 means?

Answer 21

I mean, do you understand what that number represents?

Answer 22

It means that he falls in with the scores of %65.9 of his class?

Answer 23

not quite, it means that he scored better than 65.9% of the other students

in order for Marcus to be in the top 2% and get the certificate, he needs to score better than 98% of all the other students

so, do you think he got the certificate?

Answer 24

Ooh, ok! :) Nope, he didn't.

Answer 25

great, we've answered the question!

good job

Answer 26

Yay! Thank you so much @Vocaloid

Answer 27

I fanned and medaled :)

Answer 28

thanks, I really appreciate it ^ ^

Answer 29

Np :) ttyl!