Question

Scores in a standardized exam are normally distributed with mean μ = 510 and standard deviation σ = 60. The middle 75% of scores are classified as “average”. Find the range of scores that are average according to this definition.

Answer 1

$\mu=510,\sigma=60$

Middle 75% are classified as avergae-

$\alpha=0.25$

$z_{\frac{\alpha}{2}}=z_{0.125}=1.1503$

Confidence Interval $= \mu\pm z_{0.125}\times 60$

$=510\pm 1.1503\times 60\\=(510\pm 69.018)\\=(440.98,579.018)$