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Answer:
The expected value of X is 2 with a standard deviation of 1.34.
Step-by-step explanation:
For each speaker, there are only two possible outcomes. Either it is defective, or it is not. The probability of a speaker being defective is independent of other speakers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Stereo speakers are manufactured with a probability of 0.1 of being defective
This means that
Twenty speakers are randomly selected.
This means that
Let the random variable X be defined as the number of defective speakers. Find the expected value and the standard deviation.
The expected value of X is 2 with a standard deviation of 1.34.