3, 1-을6. +9. 1-(급+음12. 37 -27
1 answer:
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Answer:
Mean: 0.9 pistons
Standard deviation: 0.944 pistons
Step-by-step explanation:
Either a piston is defective, or it is not. This means that for either piston, there can only be two outcomes. This means that we can solve this problem by the binomial distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and each trial can only have two outcomes, with probabilities and
.
For an experiment with n repeated trials and a probability of success , we have that:
The mean is:
The standard deviation is:
In this problem
There are 90 pistons, so .
There is a 1% probability that a piston is defective, so .
Estimate the number of pistons in the sample that are defective by giving the mean of the relevant distribution:
Quantify the uncertainty of your estimate by giving the standard deviation of the distribution.