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Mathematics - Finite Mathematics

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Note the similarities in the following parallel treatments of a frequency distribution and a probability distribution.

Frequency Distribution
Complete the table below for the following data. (Recall that x is the midpoint for the interval.)
14,7,1,11,2,3,11,6,10,13,11,11,16,12,9,11,9,10,7,12,9,6,4,5,9,16,12,12, 11,10,14,9,13,10,15,11,11,1,12,12,6,7,8,2,9,12,10,15,9,3
Interval x Tally f x*f f*x2
1-3 2 |||| | 6 12 24
4-6
7-9
10-12
13-15
16-18
Totals
Probability Distribution
A binomial distribution has n = 10 and p = .5. Complete the following table.
x P(x) x*P(x)
0 .001
1 .010
2 .044
3 .117
4
5
6
7
8
9
10
Totals

a. Find the mean (or expected value) for each distribution.
b. Find the standard deviation for each distribution.
c. (Extra credit) Use the normal approximation of the binomial probability distribution to find the interval that contains 95.44% of that distribution.

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In the textile industry, filament and yarn sizes are reported in denier which is defined as the mass in grams of a length of 9000 meters. If a synthetic fiber has an average specific gravity of 1.32 and a filament of this material has a denier of 5.0, what is the mass per unit length in pounds-mass per yard? What is the cross sectional area of this fiber in square inches? The specific gravity is defined as specific gravity = density/density of water.

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