Question

# 3. [16 pts] Suppose that the birth weight of puppies follows a certain left-skewed distribution with...

3. [16 pts] Suppose that the birth weight of puppies follows a certain left-skewed distribution with mean 1.1 pounds and standard deviation 0.14 pounds (these numbers are made-up). We are interested in looking at the mean weights of samples of size n puppies. We would like to model these mean weights using a Normal Distribution.

a. [3 pts] What statistical concept allows us to do so and what is the sample size

requirement?
Now suppose that we take sample of size n = 35 puppies and calculate the mean.

b. [4 pts] How are these means distributed? (Express the distribution using statistical notation.)
c. [4 pts] What is the probability that the mean birth weight of 35 randomly chosen puppies is between 0.5 pounds and 1.77 pounds? Show your work.

d. [5 pts] 1.2 ∗ 10−5% of the puppies are expected to weight more than x pounds at birth. What is x? Show your work.

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