Use the normal distribution of SAT critical reading scores for which the mean is 507 507 and the st

a)

P(X < 550)

Normal Distribution, µ = 507, σ = 122, we convert this to standard normal using

\(z=\frac{x-u}{σ}\)

\(z=\frac{550-507}{122}\)

z= 0.352459 ≈ 0.35

P(X < 550) = P(Z < 0.35) =  0.6368(from z-table)
P(Z < o.35): in a z-table having area to the left of z, locate 0.3 in the left most column. Move
across the row to the right under column 0.05 and get value  0.6368


b)

Normal Distribution, µ = 507, σ = 122, we convert this to standard normal using


\(z=\frac{x-u}{σ}\)

\(z=\frac{525-507}{122}\)

z= 0.14754 ≈ 0.15

P(X > 525) = P(Z > 0.15) = 1 − P(Z < 0.15) = 1 − 0.5596 = 0.4404

P(Z < 0.15): in a z-table having area to the left of z, locate 0.1 in the left most column. Move
across the row to the right under column 0.05 and get value 0.5596