Question

3. (14 pts) A box contains three $1 bills, two $5 bills, five $10 bills, and one $20 bill. Construct a probability distribution for the data if x represents the value for a single bill drawn at random and then replaced. Find the mean, variance, and standard deviation (1

Answer 1

Let the value of bills is denoted by random variable, X. Given that there are three $1 bills, two $5 bills, five $10 bills and one $20 bill. Then, total number of bills = 3 + 2 + 5 + 1 = 11 Probability of selecting $1 bill = Probability of selecting $5 bill = Probability of selecting $10 bill. 1 - Elu Probability of selecting $20 bill = P(X) 3/11 2/11 5:11 111

=  1 * 3/11 + 5 * 2/11 + 10 * 5/11 + 20 * 1/11 = 0.27+0.90+4.54+1.81 = 7.5

Mean = ΣΤΡ(at)

Consider,

E(X2) =Σ? Ρ(at

= 1² * 3/11 + 5² * 2/11 + 10² * 5/11 + 20² * 1/11 = 0.27+4.54+45.45+36.36 = 86.6

Now, Consider,

Variance = E(X) - (Mean)

=86.6 - 7.5²

=86.6-56.25

=30.4

Consider,

   = √30.4 = 5.5

SD= V variance