Statistics question

Question

A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 7. If James z - score is 1.20and John got 84on the test answer the following questions:

a) What’s Jane’s score on the test?

b) What’s John’s Z score?

c) What percentage of the students’ scores fall between Jane and John’s scores?

Answer 1

z = (x - mean)/SD

where x is score

z = (x - 100)/7

a) if z - score is 1.2 then

1.2 = (x - 100)/7

x = 100.4

b) if x = 84

z = (84 - 100)/7

z = 2.29

c) P(1.2 < z < 2.29) = P(z < 2.29) - P(z < 1.2) = 0.9890 - 0.8849 = 0.1041