1. Normal Distribution Computations: A certain manufacturer produces batteries for cell phones. These batteries have a life expectancy that is normally distributed with a mean of 5 hours and a standard deviation of 1 hour.

a) What is the probability that a randomly selected battery will last between 2 and 4 hours?

b) What is the probability that a randomly selected battery will last longer than 5 hours?

c) A researcher collects a random sample of batteries of size 36 then records the sample average. They repeat this process 100 times recording the sample averages each time. Assuming independent sampling with replacement, what will (theoretically) be the mean of the sample averages be?

2. Central Limit Theorem Concept: 
Pretend I am a high school student who knows absolutely nothing about Statistics. Explain the Central Limit Theorem to me simply in a way that I can understand.
3. Sampling Distribution: 
The birth weight of boy babies of European descent who were delivered at 40 weeks is normally distributed with a mean of 3687.6 g with a standard deviation of 410.5 g (Janssen, Thiessen, Klein, Whitfield, MacNab & Cullis-Kuhl, 2007). Suppose there were nine European descent boy babies born on a given day and the mean birth weight is calculated.
a) What is the mean of the sample mean?
b) What is the standard deviation of the sample mean?
c) What distribution is the sample mean distributed as? What theorem are you using?
d) Find the probability that the mean weight of the nine boy babies born was less than 3500.4 g.
e) Create a 95% confidence interval around the mean for that group.
4.Conceptual questions: Complete the following concept questions from the book, in Chapter 3:

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