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1. Suppose you have 4 nickels, 6 dimes, and 4 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that

a. You will draw a dime?

b. You will draw a nickel?

c. You will draw a quarter?

2. You are rolling a pair of dice, one red and one green. What is the probability of the following outcomes:

a. The sum of the two numbers you roll from the dice is 11.

b. The sum of the two numbers you roll is 6.

c. The sum of the two numbers you roll is 5.

3. A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble? a green marble? a blue marble? a yellow marble?

Case assignment expectations:

The following items will be assessed in particular:

Identify the meaning of independent and dependent events.
Calculate probabilities and joint probabilities of simple events.
Explain the basic logic of probability theory

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Arithmetic mean, median and probablity

1. A property of concern for any food company that uses a high-speed carton-filling machine to package juice is the weight of the food product in the individual cartons. If the cartons are under filled, two problems arise. First, customers may not have enough product for their needs. Second, the company may be in violation of the truth-in-labeling laws. In this example, the label weight on the package indicates that, on average, there are 2.5 ounces of product in a carton. If the average amount of product in a carton exceeds the label weight, the company is giving the product for free. Getting an exact amount of product in a carton is problematic because of variation in the temperature and humidity inside the factory, differences in the density of the product, and the extremely fast filling operation of the machine (approximately 450 cartons per minute). The following table provides the weight in ounces of a sample of 60 cartons produced in one hour by a single machine:

4.01 4.06 2.45 2.06 2.02 2.59 2.72 3.08 3.08 3.04
2.22 2.47 2.96 2.41 2.42 2.09 3.03 3.09 1.98 3.05
3.11 2.31 1.28 3.01 2.42 2.49 1.57 2.46 2.55 2.52
3.02 1.87 1.99 1.88 1.38 3.06 3.04 3.04 3.07 2.52
3.08 3.03 1.62 2.32 1.43 2.12 2.43 2.99 1.85 3.08
3.04 3.11 1.59 1.81 3.02 2.99 3.01 1.76 3.01 2.33

a. Compute the arithmetic mean and median.
b. Compute the first quartile and third quartile.
c. Compute the range, interquartile range, variance, standard deviation, and coefficient of variation.
d. Interpret the measures of central tendency within the context of this problem. Why should the company producing the bottles be concerned about the central tendency?
e. Interpret the measures of variation within the context of this problem. Why should the company producing the bottles be concerned about variation?

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