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Your wallet contains two $1 bills, four $5 bills, six $10 bills and 8 $20 bills.

ID: 3356636 • Letter: Y

Question

Your wallet contains two $1 bills, four $5 bills, six $10 bills and 8 $20 bills.

a.) Construct a probability distribution for the data for randomly selecting one of the bills (assume that the bill will be replaced after each draw).

b.) Calculate the mean, variance and standard deviation for the distribution. Please show your steps and use the equation editor to format your answers. Mean( Variance: Standard Deviation:

c.) Use the range rule of thumb to determine if it would it be considered unusual to pull a $1 bill out of your wallet? Explain.

Explanation / Answer

Here two $1 bills,four $5 bills, six $10 bills and eight $ 20 bills.

Total bills = 2 + 4 + 6 + 8 = 20

(a) Here probability distriubtion for the data for randomy selecting one of the bills.

Pr($1 bill) = 2/20 = 0.1

Pr($5 bill) = 4/20 = 0.2

Pr ($ 10 bill) = 6/20 = 0.3

Pr($ 20 bill) = 8/20 = 0.4

(b) Mean = 0.1 *1 + 0.2 * 5 + 0.3 * 10 + 0.4 * 20 = $ 12.1

Variance = 0.1 * (12.1 - 1)2  + 0.2 * (12.1 - 5)2 + 0.3 * (12.1 - 10)2 + 0.4 * (12.1 - 20)2 = 48.69

Standard deviation = sqrt (variance) = sqrt(48.69) = $ 6.98

(c) Range ruleof thumb = Lower limit = 12.1 - 2 * 6.98 = $ (-1.86)

so $1 bill is above the lower init as per range rule of thumb so it would not be unusual to pull a $1 bill out of wallet.