Question

The probabilities that a customer selects 1, 2, 3, 4, or 5 items at a store are 0.32, 0.12, 0.23, 0.18, and 0.15, respectively. a) Verify that this is a legitimate probability distribution. b) Find the mean number of items selected. c) Find the standard deviation of the number of items selected.

Answer 1

Answer:

a. This is a probability distribution as ∑pi=1

b. 2.72

c. 1.45

Step-by-step explanation:

a. To verify the probability distribution we simply add all given probabilities and see whether they sums up to 1 or not. According to definition of probability distribution sum of probabilities should be 1 so,

∑pi=0.32+0.12+0.23+0.18+0.15=1

Hence it is verified that given distribution is a probability distribution.

b. Mean number of items selected= E(x)= ∑x*p(x)

here x =1,2,3,4,5 and p(x)=0.32,0.12,0.23,0.18,0.15.

mean number of items=1*0.32+2*0.12+3*0.23+4*0.18+5*0.15=2.72

c. standard deviation of number of items=sqrt[(∑x²*p(x))-(∑x*p(x))²]

∑x²*p(x)=1*0.32+4*0.12+9*0.23+16*0.18+25*0.15=9.5

(∑x*p(x))²=(2.72)²=7.4

standard deviation of number of items=sqrt[(∑x²*p(x))-(∑x*p(x))²]=sqrt(9.5-7.4)=sqrt(2.1)=1.45