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Westkost [7]
3 years ago
7

The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is s

trongly skewed to the right. The central limit theorem says that
(a) as we look at more and more bulbs, their average burnout time gets ever closer to the mean m for all bulbs of this type.
(b) the average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution.
Mathematics
1 answer:
liubo4ka [24]3 years ago
6 0

ANSWER:

The average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.

STEP-BY-STEP EXPLANATION:

The cental limit theorem states, that id the sample size is large (30 or more), then the sampling distribution of the sample means is approximately normal with mean ц and standar deviation б/\sqrt{n}

Thus the correct answer is the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.

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Answer: 0.14

Step-by-step explanation:

Given: Mean : \lambda=15\text{ per seconds}

In minutes , Mean : \lambda=4\text{ per minute}

The exponential distribution function with parameter \lambda  is given by :-

f(t)=\lambda e^{-\lambda t}, \text{ for }x\geq0

The probability of waiting more than 30 seconds i.e. 0.5 minutes is given by the exponential function :-

P(X\geq0.5)=1-P(X\leq0.5)\\\\=1-\int^{0.5}_{0}4e^{-4t}dt\\\\=1-[-e^{-4t}]^{0.5}_{0}\\\\=1-(1-e^{-2})=1-0.86=0.14

Hence, the probability of waiting more than 30 seconds = 0.14

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Step-by-step explanation:

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1. What is the slope of the line tangent to the curve defined by y2 + xy - x2 = 11x at the point (2, 3)?
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Step-by-step explanation:

By using Implicit Differentiation,

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=> dy/dx = (11 + 2(2) - (3)) / (2(3) + (2))

= 12 / 8 = 1.5.

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Step-by-step explanation:

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