# Mathematics

Forest Green Brown, Inc., produces bags of cypress mulch. The weight in pounds per bag varies, as indicated in the accompanying table

a. Graph the probability distribution.

b. Calculate and graph the cumulative probability distribution.

c. What is the probability that a randomly chosen bag will contain more than 45 and less than 49 pounds of mulch (inclusive)?

d. Two packages are chosen at random. What is the probability that at least one of them contains at least 47 pounds?

e. Compute—using a computer—the mean and standard deviation of the weight per bag. f. The cost (in cents) of producing a bag of mulch is 75 + 2X, where X is the number of pounds per bag. The revenue from selling the bag, regardless of weight, is $2.50. If profit is defined as the difference between revenue and cost, find the mean and standard deviation of profit per bag.

- 5
A random sample was taken of the thickness of insulation in transformer windings, and the following thicknesses (in millimeters) were recorded:

18 21 22 29 25 31 37 38 41 39 44 48 54 56 56 57 47 38 35 36 29 37 32 42 43 40 48 36 37 37 36 38 40 41 44 39 38 34 24 32 39 44 42 30 37 30 42 37 34 37 32 24 42 36 49 39 23 34 36 40 a) Make a stem-and-leaf display for these data. Show at least five stems. Sort the data on each stem in order of increasing magnitude.

b) Estimate from these data the percentage of all the windings that received more than 30 mm of insulation but less than 50 mm.

c) Find the median, lower quartile, and ninth decile of these data.

d) Make a frequency table for the data. Use Sturges’ rule.

e) Draw a frequency histogram.

f) Add and label an axis for relative frequency.

g) Draw a cumulative frequency graph.

h) Find the mode.

i) Show a box plot of these data.