Mean is 80 standard deviation is 3 what percentage of scores would fall between 78 and 83

Answer 1

Let x = score, want to find P(78 < x < 83)

x is N(80, 3)

Modify range of above inequality to standard normal distribution N(0,1) using transformation

z = (x - mean)/SD = (x - 80)/3

Compute for x = 78

z = (78 - 80)/3 = -0.67

Compute for x = 83

z = (83 - 80)/3 = 1

P(78 < x < 83) = P(-0.67 < z < 1) = P(z < 1) - P(z < -0.67) 0.8413 - 0.2514 = 0.5899

58.99%