The probability that a DVD player produced by VCA Television is defective is estimated to be 0.07. A sample of ten players is selected at random. What is the probability that the sample contains no defective units?
What is the probability that the sample contains at most two defective units?
What is the probability that the sample contains at most two defective units?
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The probability that the sample contains no defective units can be calculated using the binomial probability formula, which is:
[ P(X = k) = \binom{n}{k} \times p^k \times (1-p)^{n-k} ]
Where:
- ( n ) is the number of trials (in this case, the number of DVD players in the sample, which is 10).
- ( k ) is the number of successes (in this case, the number of non-defective DVD players, which is 10 since we want the sample to contain no defective units).
- ( p ) is the probability of success on each trial (in this case, the probability that a DVD player is not defective, which is ( 1 - 0.07 = 0.93 )).
Plugging these values into the formula:
[ P(X = 10) = \binom{10}{10} \times (0.93)^{10} \times (0.07)^{0} ]
[ P(X = 10) = 1 \times (0.93)^{10} \times 1 ]
[ P(X = 10) = (0.93)^{10} ]
Calculating this value gives:
[ P(X = 10) \approx 0.478 ]
So, the probability that the sample contains no defective units is approximately ( 0.478 ) or ( 47.8% ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- What is a binomial distribution?
- The probability that a DVD player produced by VCA Television is defective is estimated to be 0.07. A sample of ten players is selected at random. What is the probability that the sample contains no defective units?
- Three manufacturing plants, say I, II and III, produce 20, 30 and 50 percent of a company’s output respectively. What is the probability that a randomly-chosen item from the company’s warehouse is defective?
- A coin is tossed 16 times. What is the probability of obtaining exactly 14 heads?
- What is APY(Annual Percentage Yield)? How is the APY compounded semiannually at #15%#, different from the same amount compounded continuously at #14%#?

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