# 1. Basic Business Math: a. Suppose that \$532,000 is to be allocated for advertising, research, and i

1. Basic Business Math:   a.   Suppose that \$532,000 is to be allocated for advertising,   research, and investment in the ratio 8:7:4 .  How much money will be   allocated for each?

b. Home Depot sells boxes of high quality ceramic tile (\$98 box)   and vinyl tile boxes (\$40 each).  In June, total sales were \$79500.   Customers bought 5 times as many boxes of ceramic tile as vinyl tile.    How many of each did Home Depot sell?

4.    A well known teddy bear manufacturing company maintains   records concerning the number of unacceptable bears obtained from the   stuffing and seaming machines.  Based on past data, the probability that   a bear came from machine I and was nonconforming is 0.04 and the probability   that a bear came from machine II and was nonconforming is 0.06.  These   probabilities represent the probability of one bear out of the total sample   having the specified characteristics.  Half the bears are stuffed and seamed   on machine I and the other half are stuffed and seamed on machine II.    a. If a stuffed bear is   selected at random, what is the probability that it is a nonconforming   bear?    b. If a stuffed bear is   selected at random, what is the probability that it was stuffed on machine   II?    c. If a stuffed bear is   selected at random, what is the probability that it was stuffed on machine I   and is a conforming bear?

3.  A quality   characteristic of interest for a tea-bag-filling process is the weight of the   tea in the individual bags.  If the bags are under filled, two problems   arise.  First, customers may not be able to brew the tea to be as strong   as they wish.  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 3.40 grams of tea in a   bag.  If the average amount of tea in a bag exceeds the label weight,   the company is giving away product.  Getting an exact amount of tea in a   bag is problematic because of variation in the temperature and humidity   inside the factory, differences in the density of the tea, and the extremely   fast filling operation of the machine (approximately 215 bags a   minute).  The following table provides the weight in grams of a sample   of 50 bags produced in one hour by a single machine:           2.25 3.7 3.42 3.4   3.57 3.4 3.83 2.54   3.67 3.4 3.47 3.61   4.78 3.57 3.42 3.58   3.75 3.45 3.44 3.25         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 tea bags be concerned   about the central tendency?    e.   Interpret the measures of variation within the context of this problem.    Why should the company producing the tea bags be concerned about   variation?