Question

1. 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

Calculating the z scores for each student:
     zTara = (52-64 )/8 = -12/8 = -1.5
     zJamal  = (82-64)/8 = 18/8 = 2.25
     zSamuel = (66-64)/8 = 2/8 = 0.25
From the z score table, the probability of Tara's score being greater than -1.5 is 0.0668. Therefore, the percentage is 0.0668*100 = 6.68% which means that around 7% of the students got a better mark than Tara, with 93.32% of the students scoring lower than her.
The probability of Jamal's score being greater than 2.25 is 0.0122, therefore the percentage is 0.0122*100 = 1.22% implying that around 1% of the students got a better mark than Jamal.
The probability of Samuel's score being greater than 0.25 is 0.4013, therefore the percentage is 0.4013*100 = 40.13% which means that around 40% of the students got a better mark than Samuel, with 59.87% of the students scoring lower than him.