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snow_lady [41]
4 years ago
8

Lucas is riding his bike to the park which is 2 kilometersfrom his house. When he is one-fourth of the way tothe park, it starts

to rain. Lucas turns around and ridesback home. How many meters did Lucas ride?st Practice

Mathematics
1 answer:
Evgesh-ka [11]4 years ago
4 0
Lucas rode 1,000 meters b/c 
2 klm is = to 2000 meters.
and 1/4 of 2000 meters is 500 meters but then he had 
to turn back to go home so that's another 500 meters and in total he rode 1,000 meters.
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Answer:

For the exponential distribution:

\mu = \frac{1}{\lambda}

\sigma^2 = \frac{1}{\lambda^2}

We know that the exponential distribution is skewed but the sample mean for this case using a sample size of 60 would be approximately normal, so then we can conclude that if we have a sample size like this one and an exponential distribution we can approximate the sample mean to the noemal distribution and indeed use the Central Limit theorem.

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Step-by-step explanation:

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

For this case we have a large sample size n =60 >30

The exponential distribution is the probability distribution that describes the time between events in a Poisson process.

For the exponential distribution:

\mu = \frac{1}{\lambda}

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We know that the exponential distribution is skewed but the sample mean for this case using a sample size of 60 would be approximately normal, so then we can conclude that if we have a sample size like this one and an exponential distribution we can approximate the sample mean to the noemal distribution and indeed use the Central Limit theorem.

\bar X \sim N(\mu_{\bar X} , \frac{\sigma}{\sqrt{n}})

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