statistics

1) Find the following probabilities:

a)     P (0 ≤ Z ≤ .5)

b)     P (Z ≤ .5)

c) P (Z ≤ -.5)

d) P (Z ≥ .5)

e) P (- .5 ≤ Z ≤ .5)

2) Dearborn Tech produces a circuit board that has an average life span of 4,500 hours. The life span is normally distributed with a standard deviation of 500 hours. The firm is considering a 3,800 hours’ warranty on the circuit board. If this warranty policy is adopted, what proportion of circuit boards should the firm expect to replace under warranty?