Question

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 a letter to Marcus explaining whether or not he will be receiving a certificate. Include a brief summary of your statistic

Answer 1

1 know he is not going to receive a certificate but 1 don't know why.

Answer 2

how far is marcus score from the mean scores? or rather, how many standard deviations is it from the mean scores?

Answer 3

if the z score (the number of standard deviations) for marcus' score does nto exceed the z score related to the 98% marker .... then he fails to get past the goal ...

Answer 4

tell me how we determine these two z values for comparison ...

Answer 5

do you have a ti83 by chance? or do you have to rely on tables?

Answer 6

sorry mini crisis 1'm back.

Answer 7

1 know the average score but 1 don't know what the top 2% would be.

Answer 8

@amistre64

Answer 9

thats why we need to know the z score related to our boundary (98% : 2%)

and the z score related to our test score itslef

lets say the boundary is given as: 2.054

if test value is less then this, we are in the 98%, if its higher, we are in the 2%

so we need to determine how many standard deviations the test score is from the mean score ...

(test - mean)/sd

Answer 10

the mean score is 12.89 with a deviation of 1.95, so between 14.84 and 10.94

Answer 11

13.7 - 12.89 is how much?

Answer 12

or we dont really need to go that route sdo we ... if we know the boundary itslef

mean + z(sd)

12.89 + 2.054(1.95) is the cutoff

Answer 13

scores of 16.89 and above are required ....

Answer 14

where did 16.89 come from?

Answer 15

i spose the question is, how do we find the z score for the boundary ....

Answer 16

well you know where 12.69 came from, and you know the measurement we are using is 1.95 .... we are trying to determine how many (1.95)s there are between the mean and the cutoff of 98%

Answer 17

what do you have to work with? ti83 or tables?

Answer 18

1 have a ti-30xs

Answer 19

ti-30xs isnt going to be useful for this. thats a financial calculator i believe

Answer 20

1t's all 1've got :/

Answer 21

then you dont have the tools needed to answer the question. your course should provide you with at least a table to work with.

we can use the wolf ... but if you take a test you aint gonna have that are you

Answer 22

what kind of table are you talking about a z table?

Answer 23

yes, a z table

Answer 24

there was one earlier in the lesson 1 can go back and find it

Answer 25

we can use this, but we will have to modify the results ....

look in the feild and find a value closest to .0200

Answer 26

-2 0.5

Answer 27

good, now this is on the wrong side of the mean .. its a left tail measure related to the bottom 2% :)

jsut get rid of that negative and we will be fine

Answer 28

can 1 do that?

Answer 29

z = 2.05

Answer 30

of course ... the symmetry of the normal distribution tells us that the area above z=k and the area below z=-k are equal

Answer 31

so what do 1 do with 2.05?

Answer 32

that is the number of standard devaitions from the mean that is our boundary

mean + 2.05(sd) is the cutoff scores

Answer 33

ah