You are allowed to use your calculator. Explain all answers – answers with no explanation will receive only partial credit. Use complete sentences. Show how you used the calculator to answer the questions below.
| Name | Age | Name | Age | Name | Age |
| William | 37 | Michael | 41 | James | 28 |
| Jack | 39 | Kathy | 41 | Kate | 29 |
| Patty | 30 | Eileen | 22 | Mary | 40 |
| John | 45 | Joseph | 49 | Rene | 32 |
| Sophie | 46 | Julia | 34 | Anthony | 35 |
1. Construct an SRS of 5 from the above list of people. Explain clearly how you constructed the SRS. What is the mean age of your sample? Answer
2. A food company is preparing to market a new cake mix. It is important that the taste of the cake
not be changed by small variations in baking time or temperature. In an experiment, cakes are made from the mix
are baked at 300 degrees, 320 degrees and 340 degrees F, and for 1 hour and 1 hour and 15 minutes. Ten
cakes are baked at each combination of temperature and time. A panel of tasters scores each cake for texture
and taste.
(a). What are the experimental units?
(b). What are the explanatory variables and response variables for this experiment?
(c). What are the factors and their levels?
(d). Outline the design of the experiment.
Answer
3. Two fair regular six-sided die are rolled. List the sample space. Let X be the sum of the random roll of the die.
Find the following probabilities:
(a). P(X<2)
(b). P(X≥7)
(c). P(X≤11)
(d). P(X<11)
(e). P(X=5)
(f). P(X=5 or X>10)
Answer
4. List the sample space of children of a four-child family. Find the following probabilities:
(a). P(exactly 3 boys)
(b). P(exactly 2 girls)
(c). P(at least 2 boys)
(d). P(at most 2 girls)
Answer
5. A supervisor has determined that the salary of employees in his department is normally distributed with a mean of
$30,000 and a standard deviation of $15,000. A sample of 30 of the employees' salaries was selected at random. Let X be
the mean of the sample. Find the following probabilities:
(a). P(X=25,000)
(b). P(X>25,000)
(c). P(20,000<X<30,000)
(d). P(X>35,000)
Answer
6. An electron is expelled from a source in the direction of 2 detector devices. The probability that the electron is detected by the first device is 0.5 and the probability that the electron is detected by the second device is 0.5. Construct an experiment that will count the number of times the first 100 electrons is detected by the first device. Answer