Question

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?

Answer 1

idnt understand yuur question

Answer 2

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<1.808) which is same P(x <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 <Z < 0.678) = P(Z<.678) - P(Z<-1.58)