Question

Exercise 1: In a certain population of mussels (Mytilus edulis), 80% of the individuals are infected with an intestinal parasite. A marine biologist plans to examine 100 randomly chosen mussels from the population. Find the probability that 85% or more of the sampled mussels will be infected. Exercise 2: A data analyst is given a random sample of size 25 from a normal population of telephone pole lengths. Let $\mu$ and $\sigma^2$ denote the expected value and variance of this population, respectively. 1. If this data analyst is interested in estimating the population parameter $\theta = \frac{3}{2}\mu + \frac{1}{2}\sigma^2$, find the point estimator of $\theta$. What is its sampling distribu- tion? 2. If it is known that 90.32% of the sample means are less than 10 feet in length and 88.49% of the sample means are greater than 5 feet in length, find $\mu$ and $\sigma^2$

          Exercise 1:
In a certain population of mussels (Mytilus edulis), 80% of the individuals are
infected with an intestinal parasite. A marine biologist plans to examine 100
randomly chosen mussels from the population. Find the probability that 85%
or more of the sampled mussels will be infected.
Exercise 2:
A data analyst is given a random sample of size 25 from a normal population
of telephone pole lengths. Let $\mu$ and $\sigma^2$ denote the expected value and variance
of this population, respectively.
1. If this data analyst is interested in estimating the population parameter
$\theta = \frac{3}{2}\mu + \frac{1}{2}\sigma^2$, find the point estimator of $\theta$. What is its sampling distribu-
tion?
2. If it is known that 90.32% of the sample means are less than 10 feet in
length and 88.49% of the sample means are greater than 5 feet in length,
find $\mu$ and $\sigma^2$

Exercise 1:
In a certain population of mussels (Mytilus edulis), 80% of the individuals are
infected with an intestinal parasite. A marine biologist plans to examine 100
randomly chosen mussels from the population. Find the probability that 85%
or more of the sampled mussels will be infected.
Exercise 2:
A data analyst is given a random sample of size 25 from a normal population
of telephone pole lengths. Let μ and σ^2 denote the expected value and variance
of this population, respectively.
1. If this data analyst is interested in estimating the population parameter
θ = (3)/(2)μ + (1)/(2)σ^2, find the point estimator of θ. What is its sampling distribu-
tion?
2. If it is known that 90.32% of the sample means are less than 10 feet in
length and 88.49% of the sample means are greater than 5 feet in length,
find μ and σ^2

Added by Hector S.

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