Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked.

probability x is at most 30? less than 30? between 15 and 25?

P = 0.11

1-p =.89

n = 200

mean = n*p = 22

std dev = n*sqrt (p (1-p) / n) = 4.425

find z values for standard normal distribution

Z = (30-22) / 4.425 = 1/808

look up table to find P (Z less than 1.808) which is same P (x less than 30)

for 2nd part, you need 2 Z values

Z1 = (25-22) / 4.425 = 0.678

Z2 = (15-22) / 4.425 = - 1.58

P (-1.58 less than Z less than 0.678) = P (Z less than. 678) - P (Z less than - 1.58)