The scores on a math test are normally distributed with a mean of 64

Question

The scores on a math test are normally distributed with a mean of 64 and a standard deviation of 8. Tara scored 52 on the test . jamal scored 82 on the test. Samuel scored 66 on the test . find the standard (z) score for each student and answer the questions. 

A. What percent of students did tara score better than?

B. What percent of students scored better than jamal?

C. What percent of students did Samuel score better than ?

Answer 1

 

Using the z-score formula

z=( x  - μ) / σ

 

Where x represents score of particular student  , the mean is represented by μ and standard deviation by σ .

 

Z _Tara = (52 -64 ) / 8 = -12/8 = -1.5

 

Z _jamal  = (82 -64)/8 = 18/8 = 2.25

 

Z _Samuel = (66 - 64 )/8 =2/8 = 0.25

 

 

Now answer the question by using z score table

Answer 2

Do you know what z scores are (formula for converting from x-data to z_x)?  

 

Do you know how to use z scores to find the probability of other students achieving ≤ that z score?

 

Review of these areas should enable you to calculate the three z scores and convert them into probabilities (and thus %s) for each student.