# Probability, Statistics, and Interest

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As the prize in a contest you are offered $1000 now or $1210 in 5 years. If money can be invested at 6% compounded annually, which is larger?

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Hello

Please find the solution in the attached file.

File - 001

Solution- (26)

(a) Since the sell in 1991 is $100,000

It growth in 5000% in next five year

Then in 1996 Sell will be = 100,000 * 5000% = $5000,000

(b) when x = 1 (1991) then y = $100,000

When x = 2 (1995), then y = $ 5000,000

Then in terms of ordered pair (1, 100,000) and (2, 5000,000).

(c) the function is linear then

Y = ax + b

When x = 1, y = 100,000

a + b = 100,000..........................(1)

when x = 2, y =5000,000

2a + b = 5000,000

Then a = 4900,000

And b = - 4800,000 (substituting it in (1) )

Then linear function

Y = 4900,000 x - 4800,000

(d) If it reach one billion

1,000,000,000 = 100,000*(5000%)^t

=>1,000,000,000/100,000 = (50)^t

Taking logrithm

=> t = log(10,000)/log(50) = 4/log(50 ) = 2.354 * 5 year = 11.77 year i.e in 2003

e. the actual sales expected $1 billion in 2003. If growth rate is linear then it is not possible to achieve this target because $1 billion becomes

1,000,000,000 = 100,000*5000*t/100

T = 2000 years

after 2000*5 year according to linear rate.

Solution-(18)

(a)

year Men's women's

1905 113.4 0

1915 111.9 0

1925 111.9 144

1935 109.7 135.6

1945 106.6 132

1955 105.7 125

1965 104.3 118

1975 103.7 117.48

1985 101.73 113.28

1995 101.11 113.28

According to least square method, the equation of the line is given by

y = -0.145x + 114.2

(Using MS-Excel)

(b)

According to the data, the equation of the least square line is

y = -0.449x + 151.7

(c) w omen least square line catch the men trend line,

When both equations are equal.

-0.449x + 151.7 = -0.145x + 114.2

=> -0.304x = -37.5

=> x = 123.35 years both line will meet. I don't believe it because men are more efficient rather than women.

D. by using MS-EXCEL we can ...

#### Solution Summary

Topics in this problem set include future value of money, interest, fitting situations to graphs (least squares), sets, maximizing functions, probabilities, permutations, and working with data (central tendency and standard deviation).