A company operates an assembly line. The company believes that there is a 3% probability that any given item produced on the line will contain a defect. If 100 items are pulled at random from the line, what is the probability there will be exactly 4 defective items? ____
If 100 items are pulled at random from the line, what is the probability there will be 9 or more defective items? _______
If X = the number of defectives in a sample of 100 items from the line find the mean and standard deviation of X.________
Mean of X =
Standard Deviation=
Suppose that the company did a quality control survey and did in fact pull 100 items from the line and 9 were found to be defective. Using your work above, would you question whether the "true" defect rate was actually 3%? (Select all that apply.)
No, the standard deviation of the number of defects is large relative to the mean.
Yes, the probability of obtaining 9 or more defects is quite small under the assumption of a 3% defect rate.
Yes, 9 defects is several standard deviations higher than the expected number of defects.
n =100 p=0.03
Here n>= 100, np = 100*0.03 = 3 <10 we can use poisson probabilities.
P(x = k) =
for a poisson distribution mean = variance =
a) the probability there will be exactly 4 defective items
P(X=4) = = 0.168
b) the probability there will be 9 or more defective items =
= 1- = 1- 0.996 = 0.004
c)for a poisson distribution mean = variance =
d) given 9% is defective,
Yes, the probability of obtaining 9 or more defects is quite small under the assumption of a 3% defect rate.
standard deviation = 30.5 = 1.732
mean = 3
standard deviation = 1.732
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