Answer:
The probability that more than 10 parts will be defective is 0.99989.
Step-by-step explanation:
Let <em>X</em> = a part in the shipment is defective.
The probability of a defective part is, P (Defect) = <em>p</em> = 0.03.
The size of the sample is: <em>n</em> = 1000.
Thus, the random variable .
But the sample size is very large.
The binomial distribution can be approximated by the Normal distribution if the following conditions are satisfied:
- np ≥ 10
- n (1 - p) ≥ 10
Check the conditions:
Thus, the binomial distribution can be approximated by the Normal distribution.
The sample proportion (<em>p</em>) follows a normal distribution.
Mean:
Standard deviation:
Compute the probability that there will be more than 10 defective parts in this shipment as follows:
The proportion of 10 defectives in 1000 parts is:
The probability is:
Use the standard normal table for the probability.
Thus, the probability that more than 10 parts will be defective is 0.99989.