Question

16 State whether the first area is bigger, the second area is bigger, or the two areas are equal in each of the following situations: (a) The area to the left of z 1.00 and the area (b) The area to the left of 1.00 and the area (c) The area between the mean and z 1.20 (d) The area to the left of the mean and the area (e) The area to the right of z 1.65 and the to the right of z-1.00 to the left of z-1.00 and the area to the right of z 0.80 between 2 +1.00 area to the right of z-1.65

Answer 1

A) P(Z < 1) = 0.8413

P(Z > -1) = 1 - (Z < -1) = 1 - 0.1587 = 0.8413

The two areas are equal.

B) P(Z < 1) = 0.8413

P(Z < -1) = 0.1587 = The first area is greater than the second.

C) P(0 < Z < 1.2)

= P(Z < 1.2) - P(Z < 0)

= 0.8849 - 0.5 = 0.3849

P(Z > 0.8) = 1 - P(Z < 0.8) = 1 - 0.7881 = 0.2119

So the first area is bigger.

D) P(Z < 0) = 0.5

P(-1 < Z < 1)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 01587

= 0.6826

So the second area is bigger.

E) P(Z > 1.65) = 1 - P(Z < 1.65) = 1 - 0.9505 = 0.0495

P(Z > -1.65) = 1 - P(Z < -1.65) = 1 - 0.0495 = 0.9505

So the second area is bigger.