Set of normally distributed test scores has a mean of 77 and a standard deviation of 5.

Question

Set of normally distributed test scores has a mean of 77 and a standard deviation of 5. (Draw distribution and indicate each value)

a. What is the probability that normally selected score will be between 77.5 and 80.3?

b. What percent of test scores fall below the grade of 80.6?

c. What percent of test scores will be above a grade of 80.6?

Answer 1

x = test score, N(77,5)

z = (x - mean)/SD is N(0,1)

a)

P(77.5 < x < 80.5) = P( (77.5 - 77)/5 < z < (80.3-77)/5) = P(0.1 < z < 0.65) = P(z < 0.65) - P(z < 0.1)

Lookup probabilities from standard normal probability table

b)

P(x < 80.6) = P(z < (80.6 - 77)/5) = P(z < 0.72)

c)

P(x > 80.6) = 1 - P(x < 80.6)