Question

The scores on a math test are normally distributed. If the mean is 72 and the standard deviation is 6, what is the range of 98% of the scores?

		54-84
		54-90
		60-84
		66-84

Answer 1

The scores on a math test are normally distributed. If the mean is 72 and the standard deviation is 6.

Since Option B and Option C are range for within 3 standard deviation and 2 standard deviation respectively. SO ELIMINATE OPTION B AND C

Pr(54≤X≤90)≈0.997

μ−3σ=72−3×6=54
μ+3σ=72+3×6=90

Pr(60≤X≤84)≈0.95

Also Option D cannot be the answer because its value covering 81.8%

So Option A would be the answer.

Pr(54≤X≤84)=Pr(X≤84)−Pr(X≤54)
\approx 0.975 - 0.0015 = 0.9735
≈0.975−0.0015=0.9735