Tire pressure = 32 psi. The warning system will alert the driver when the tire pressure is 25% below the target pressure.

A. At what tire pressure will the warning system alert the driver? My answer: 32 x .25 = 8 so, 32 - 8 = 24 psi. (my answer is correct)

B. Standard deviation of a normally distributed tire pressure = 3 psi. If tire pressure is on target, what is the probability of a system warning?

P (x < 24) = P (x-mean/sd) < 24 - 32/3 = P (z < -2.67) = .0038 (my answer is correct)

C. Recommended inflation is 30 - 34 psi. Assume psi is on target. If a tire is inspected at random, what is the probability that the tire's inflation is within the recommended range?

So, P(30 < x < 34) = P(30 - 32)/3 < x - mean/sd < 34 - 32/3

= P (-0.67 < z < 0.67)

= P (z < 0.67) - P (z < -0.67)

= 0.7486 - 0.2514

= 0.4972 (my answer is incorrect)

Please show calculations and answers. (Answer C requires both the intermediate and final calculations to be rounded to 4 decimal places.)