Question

Scores of an achievement test show that it follows a normal distribution. Its mean is 78 with a standard deviation of 8. Find the interval wherein the middle 80% of the score lie.

Answer 1

µ = 78

σ = 8

Middle probability is 0.8, so left tailed probability is 0.1

P(X < x) = 0.1

P(Z < z) = 0.1

Using technology, z = –1.28

X = µ + z × σ

   = 78 + (–1.28) × 8 = 67.76

Similarly, z = 1.28 for right tailed probability

X = µ + z × σ

   = 78 + 1.28 × 8 = 88.24

So, the interval is (67.76 < X < 88.24).