Question

The scores of a recent standardized test taken by finance majors at a four-year college had an approximately normal distribution with a mean of 225 and a standard deviation of 18. Determine the probability to the nearest integer that a randomly selected test scored between 200 and 245.(1 point)
The probability that finance majors scored between 200 and 245 is
%.

Answer 1

Compute z-scores:
z1 = (200−225)/18 = −25/18 ≈ −1.389
z2 = (245−225)/18 = 20/18 ≈ 1.111

P(200≤X≤245) = Φ(1.111) − Φ(−1.389) = Φ(1.111)+Φ(1.389)−1 ≈ 0.8667+0.9175−1 ≈ 0.7842 ≈ 78%

The probability is about 78%.