5.28 A manufacturer knows that on average \( 20 \% \) of the electric toasters produced require repairs within 1 year after they are sold. When 20 toasters are randomly selected, find appropriate numbers \( x \) and \( y \) such that (a) the probability that at least \( x \) of them will require repairs is less than 0.5 ; (b) the probability that at least \( y \) of them will not require repairs is greater than 0.8 .
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- This is a binomial probability problem where we have a fixed number of trials (20 toasters), two possible outcomes (requires repair or not), and a constant probability of success (requires repair) of 0.2. Show more…
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A manufacturer knows that on average $20 \%$ of the electric toasters produced require repairs within 1 year after they are sold. When 20 toasters are randomly selected, find appropriate numbers $x$ and $y$ such that (a) the probability that at least $x$ of them will require repairs is less than 0.5 ; (b) the probability that at least $y$ of them will not require repairs is greater than 0.8 .
Some Discrete Probability Distributions
Binomial and Multinomial Distributions
A manufacturer knows that on the average $20 \%$ of the elect ric toasters which he makes will require repairs within 1 year after they are sold. When 20 toasters are randomly selected, find appropriate numbers $x$ and $y$ such that (a) the probability that at least $x$ of them will require repairs is less than 0.5 (b) the probability that at least $y$ of them will not require repairs is greater than 0.8 .
Taha T.
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