A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4.
(a) Everyone who scores in the top 30% of the distribution gets a certificate.
(b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state?
(a) Top 30% is 70% percentile
Inverse of normal distribution(0.7) = -0.5244005
Plug into z-score formula, -0.5244005 = (x - 25)/4
x = 22.9024
(b) Top 5% is 95% percentile
Inverse of normal distribution(0.95) = 1.644853627
Plug into z-score formula, 1.644853627 = (x - 25)/4
x = 31.57941451
(a) Everyone who scores in the top 30% of the distribution gets a certificate.
(b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state?
(a) Top 30% is 70% percentile
Inverse of normal distribution(0.7) = -0.5244005
Plug into z-score formula, -0.5244005 = (x - 25)/4
x = 22.9024
(b) Top 5% is 95% percentile
Inverse of normal distribution(0.95) = 1.644853627
Plug into z-score formula, 1.644853627 = (x - 25)/4
x = 31.57941451