uestion with last attempt is displayeu Tol A teacher informs his psyhcology clas

Question

uestion with last attempt is displayeu Tol A teacher informs his psyhcology class (of 500+ students) that a test was very difficult, but the grades would be curved. Scores on the test were normally distributed with a mean of 41 and a standard deviation of 7.3. The maximum possible score on the test was 100 points. Because of partial credit, scores were recorded with 1 decimal point accuracy. (Thus, a student could earn a 41.5, but not a 40.32.) The grades are curved according to the following scheme. Find the numerical limits for each letter grade. Letter Scheme Interval A |Top 6% Scores above the bottom 65% and below the top 6% scores above the bottom 35% and below the top 35% Scores above the bottom 6% and below the top 65% |Bottom 6% 30 F

Explanation / Answer

A) P(X > x) = 0.06

or, P((X - mean)/sd > ( x - 41)/7.3) = 0.06

or, P(Z > ( x - 41)/7.3) = 0.06

or, P(Z < ( x - 41)/7.3) = 0.94

or, ( x - 41)/7.3 = 1.56

or, x = 1.56 * 7.3 + 41

or, x = 52.388

b) P(X < x) = 0.65

or, P(Z < (x - 41)/7.3) = 0.65

or, (x - 41)/7.3 = 0.39

or, x = 0.39 * 7.3 + 41

or, x = 43.847

So the interval is (43.847, 52.388)

c) P(X < x) = 0.35

or, P((X - mean)/sd < ( x - 41)/7.3) = 0.35

or, P(Z < ( x - 41)/7.3) = 0.35

or, ( x - 41)/7.3 = -0.39

or, x = -0.39 * 7.3 + 41

or, x = 38.153

P(X > x) = 0.35

or, P((X - mean)/sd > ( x - 41)/7.3) = 0.35

or, P(Z > ( x - 41)/7.3) = 0.35

or, P(Z < ( x - 41)/7.3) = 0.65

or, ( x - 41)/7.3 = 0.39

or, x = 0.39 * 7.3 + 41

or, x = 43.847

so the interval is (38.153, 43.847)

d) P(X < x) = 0.06

or, P((X - mean)/sd < ( x - 41)/7.3) = 0.06

or, P(Z < ( x - 41)/7.3) = 0.06

or, ( x - 41)/7.3 = -1.56

or, x = -1.56 * 7.3 + 41

or, x = 29.612

P(X > x) = 0.65

or, P(Z > (x - 41)/7.3) = 0.65

or, P(Z < (x - 41)/7.3) = 0.35

or, (x - 41)/7.3 = -0.39

or, x = -0.39 * 7.3 + 41

or, x = 38.153

so the interval is(29.612, 38.153)

f) P(X < x) = 0.06

or, P((X - mean)/sd < ( x - 41)/7.3) = 0.06

or, P(Z < ( x - 41)/7.3) = 0.06

or, ( x - 41)/7.3 = -1.56

or, x = -1.56 * 7.3 + 41

or, x = 29.612

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