1. Draw a random sample of size 12 from a Poisson Population with mean 4 and calculate the sample mean.
What is your question?
1. Which of the following statements are correct?
a.A normal distribution is any distribution that is not unusual.b.The graph of a normal distribution is bell-shaped.c.If a population has a normal distribution, the mean and the median are not equal.d.The graph of a normal distribution is symmetric.
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A normal distribution is bell-shaped and symmetrical.
To draw a random sample of size 12 from a Poisson population with mean 4, you can follow these steps:
1. Start by understanding what a Poisson distribution is. In the context of this question, a Poisson distribution is used to model the number of events occurring in a fixed interval of time or space.
2. Calculate the probability mass function (PMF) of the Poisson distribution with a mean of 4. The PMF gives the probability of each possible number of events occurring. In this case, the PMF is P(x; λ) = (e^(-λ) * λ^x) / x!, where x is the number of events and λ is the mean (in this case, 4).
3. Using a random number generator, generate 12 random numbers between 0 and 1, representing probabilities. These random numbers will be used to sample from the Poisson distribution.
4. Calculate the cumulative distribution function (CDF) of the Poisson distribution with a mean of 4. The CDF gives the probability that the number of events is less than or equal to a given value.
5. For each of the 12 random probabilities generated in step 3, find the corresponding value of x (the number of events) using the inverse CDF method. In other words, find the value of x for which CDF(x) is closest to the random probability.
6. Repeat step 5 for all 12 random probabilities, resulting in a random sample of 12 values drawn from the Poisson distribution.
7. Calculate the sample mean by adding up all 12 values in the sample and dividing by 12. This will give you the average value of the random sample from the Poisson population.
By following these steps, you can draw a random sample of size 12 from a Poisson population with a mean of 4 and calculate the sample mean.