Answer on Statistics and Probability Question for alyssa
By assumption X has normal distribution N(8.25,0.35).
Then Z=((X-8.25)/0.35) has normal distribution N(0,1).
Then margin of error is equal to
δ = 0.35 * z, where z is such that
P(-z< Z < z) = 0.9
If Φ is a c.d.f. for N(0,1), then
z= - Φ-1 ((1-0.9)/2)= -Φ-1 (0.05)= 1.645
δ = 0.35 * 1.645 = 0.576
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