Statistics

1. (10 points) The Pizza Company claims they will deliver your in less than 30 minutes. An undercover consumer reporter monitored a random sample of 30 pizza deliveries at a National outlet. The number of minutes to perform the delivery is reported below.

44, 12, 22, 31, 26, 22, 30, 26, 18, 28, 12, 40, 17, 13, 14, 17, 25, 29, 15, 30, 10, 28, 16, 33, 24, 20, 29, 34, 23, 13.

a. Construct a stem-and-leaf display for the data set.
b. Construct a box plot for the data set.
c. Draw conclusions about the data (e.g. are there any outliers, etc., etc.).

2. (10 points) A manufacturer of PC's purchases a particular microchip, called the LS-24, from three suppliers: Ball Electronics, Zuller Sales, and Crawford Components. 30 percent of the LS-24 chips are purchased from Ball Electronics, 25 percent from Zuller Sales, and the remaining 45 percent from Crawford Components. The manufacturer has extensive histories on the three suppliers and knows that 4 percent of the LS-24 chips from Ball Electronics are defective, 5 percent of chips from Zuller Sales are defective, and 3 percent of the chips purchased from Crawford Components are defective. When the LS-24 chips arrive at the manufacturer, they are placed directly in a bin and not inspected or otherwise identified by supplier. A worker selects a chip for installation in a PC and finds it defective. What is the probability that it was manufactured by Crawford Components?

3. (10 points) Six percent of the worm gears produced by an automatic, high-speed Barter-Cell milling machine are defective.

a. Among ten randomly selected worm gears, how likely is it that only one is defective?
b. Among ten randomly selected worm gears, what is the probability that at least two are defective?
c. If the worm gears are examined one by one, what is the probability that at most five must be selected to find four that are not defective?

4. (10 points) The article "Reliability of Domestic Waste Biofilm Reactors" (J. of Envir. Engr., 1995: 785-790) suggests that substrate concentration (mg/cm^3) of influent to a reactor is normally distributed with  = 0.30 and  = 0.06.

a. What is the probability that the concentration exceeds 0.355?
b. What is the probability that the concentration is at most 0.273?
c. What is the probability that the concentration is between 0.27 and 0.31?
d. How would you characterize the largest 5% of all concentration levels?

5. (10 points) Let X1, X2, ... , X100 denote the actual net weights of 100 randomly selected 50-lb bags of fertilizer.
a. If the expected weight of each bag is 50-lb and the standard deviation is 1.5-lb, calculate P(49.5  X bar  50.25).
b. If the expected weight of each bag is 49.8-lb rather than 50-lb, so that on average bags are under-filled, but the standard deviation is still 1.5-lb, calculate P(49.5  X bar  50.25).

6. (10 points) The Arizona Wildcats baseball team, a minor league team in the Pittburgh Indians organization, plays 75% of their games at night, and 25% during the day. The team wins 55% of their night games, and 85% of their day games. According to today's newspaper, they won yesterday. What is the probability the game was played at night?