SOLUTION: The ATM at a local convenience store allows customers to make withdrawals of $10, $20, $50, or $100. Let X denote a random variable that indicates the amount withdrawn by a custome

Question 1121413: The ATM at a local convenience store allows customers to make withdrawals of $10, $20, $50, or $100. Let X denote a random variable that indicates the amount withdrawn by a customer. The probability distribution of X is
P(10) = 0.2
P(20) = 0.5
P(50) = 0.2
P(100) = 0.1
(a) Draw the probability distribution of X.
(b) What is the probability that a customer withdraws more than $20?
(c) What is the expected amount of money withdrawn by a customer?
(d) The expected value is not a possible value of the amount withdrawn. Interpret the expected value for a manager.
(e) Find the variance and standard deviation of X.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Prob >$20 is 0.3
E(X)=0.2*10+0.5*20+0.2*50+0.1*100=$32
The expected value may be considered to be a weighted average, how much will be withdrawn on average. In other words, the expected value*the number of people withdrawing will be about what the total amount of money needed is.
variance is $22^2*0.2+$12^2*0.5+$18^2*0.2+$88^2*0.1=$96.80+$72+$64.80+$774.40=$1008
sd is sqrt (V)=$31.75
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