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A certain type of flashlight requires two type-D batteries, and the flashlight will work only if both its batteries have acceptable voltages. Suppose that 90% of all batteries from a certain supplier have acceptable voltages. Among twenty randomly selected flashlights, what is the probability that at least nineteen will work? (Round your answer to three decimal places.) What assumptions did you make in the course of answering the question posed? We have assumed here that the batteries' voltage levels are independent. We have assumed here that the batteries' voltage levels are dependent.

Respuesta :

Answer:

0.392, independent

Step-by-step explanation:

Given that a certain type of flashlight requires two type-D batteries, and the flashlight will work only if both its batteries have acceptable voltages. Suppose that 90% of all batteries from a certain supplier have acceptable voltages.

For determining the probability we must assume that the batteries' voltage levels are independent

Let X be the no of batteries acceptable in the sample of 20 selected.

Then X is binomial because only two outcomes, and independence is assumed

Required proability = the probability that at least nineteen will work

=[tex]P(X\geq 19)\\\\\\=P(19)+P(20)\\=20C19 (0.9)^{19} (0.1)+(0.9)^{20}=0.27017+0.121577\\=0.392[/tex]

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