Suppose 4

Suppose that 14% 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.
a) What is the probability that X is at most 30?  
b) What is the probability that X is less than 30?  
c) What is the probability that X is between 15 and 25 (inclusive)?

Correct answer:

a =  0.6948
b =  0.6201
c =  0.3022

Step-by-step explanation:

n=200 p=14%=14100=0.14  μ=n p=200 0.14=28 σ=μ (1p)=28 (10.14)4.9071  z1=30+1/2μσ=30+1/2284.90710.5095  a=0.6948=0.6948
z2=301/2μσ=301/2284.90710.3057  b=0.6201=0.6201
c=0.3022=0.3022



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