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devlian [24]
3 years ago
7

In City Lake, researchers caught, marked, and released 258 bass. Later, they took a sample of 130 bass and found that 26 were ma

rked. Estimate the number of bass in the lake.
Mathematics
1 answer:
Vsevolod [243]3 years ago
7 0

26 out of 130 were marked.

Divide 26 by 130:

26/130 = 0.20

20% of the bass caught were tagged.

Now divide the total amount caught and tagged by that percentage:

258 / 0.20 = 1,290

There are 1,290 bass in the lake.

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Under average driving conditions, the life lengths of automobile tires of a certain brand are found to follow an exponential dis
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Answer:

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b) P(X>30000|X>15000)=P(X>15000)=1-( 1- e^{-\frac{15000}{30000}})=e^{-0.5}=0.607

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

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The cumulative distribution function is given by:

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Part a

We want to find this probability:

P(X>30000) and for this case we can use the cumulative distribution function to find it like this:

P(X>30000)=1-( 1- e^{-\frac{30000}{30000}})=e^{-1}=0.368

Part b

For this case w want to find this probability

P(X>30000|X>15000)

We have an important property on the exponential distribution called "Memoryless" property and says this:

P(X>a+t| X>t)=P(X>a)  

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We can use the definition of the density function and find this probability:

P(X>15000)=1-( 1- e^{-\frac{15000}{30000}})=e^{-0.5}=0.607

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Step-by-step explanation:

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