Data Management?

a) The shaded area lies in the extreme right tail of the normal curve

i) if you are consulting a simple z-scores chart

Total area on the right side of z = 0 is 0.5000

Area corresponding to z = 1.5 is 0.4332

Area of the shaded region = 0.5000 - 0.4332 = 0.0668

ii) if you are consulting a z-scores chart showing the area on the left side of z value

Area on the right side of z = 1.5 is equal to the area on the left side of z = - 1.5

P(z < - 1.5) = 0.0668

or

Area on the right side of z = 1 - P(z < 1.5)

= 1 - 0.9332

= 0.0668

b) i) Total area on the left side of z = 0 is 0.5000

Area corresponding to z = 1.4 = 0.4192

Area on the left side of z = - 1.4 = 0.5000 - 0.4192 = 0.0808

Total area on the right side of z = 0 is 0.5000

Area on the right side of z = 1.4 = 0.5000 - 0.4192 = 0.0808

ii) Area on the left side of z = - 1.4 = P(z < - 1.4) = 0.0808@

Area on the right side of z = 1.4 = P(z > 1.4)

= 1 - P(z < 1.4)

= 1 - 0.9192

= 0.0808@

@This is so because of the symmetry property of the normal curve