Respuesta :
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:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Stereo speakers are manufactured with a probability of 0.1 of being defective
This means that [tex]p = 0.1[/tex]
Twenty speakers are randomly selected.
This means that [tex]n = 20[/tex]
Let the random variable X be defined as the number of defective speakers. Find the expected value and the standard deviation.
[tex]E(X) = np = 20*0.1 = 2[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.1*0.9} = 1.34[/tex]
The expected value of X is 2 with a standard deviation of 1.34.
