3 years ago

Which is the best estimate for the height of a tall tree?

Mathematics

1 answer:

Ksivusya [100]3 years ago

6 0

A.) 100 Feet ...............

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A light bulb has a lifetime X that is exponentially distributed with a mean 340 hours. Find the probability that the bulb lifeti

LUCKY_DIMON [66]

Answer:

0.7026

Step-by-step explanation:

Let X denote the lifetime of light bulb. Given $X \sim Exp(\lambda)$ where the mean is $E(X) = 340 =\frac{1}{\lambda} \implies \lambda = \frac{1}{340} = 0.00294$ .

Recall that,

$\displaystyle P(X>x) = 1 - \int_0^x e^{-\lambda x} = 1 - (1 - e^{-\lambda x} = e^{-\lambda x}$

$\displaystyle P(X>220 | X>100) = \frac{P(X>220,X>100)}{P(X>100)} = \frac{e^{-\lambda \times 220}}{e^{-\lambda \times 100}} = \frac{0.5236}{0.7452} = 0.7026$