Respuesta :
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
The probability distribution, mean number, and standard deviation are 1, 2.72, and 1.45.
Probability
It is the ratio of the favorite events to the total events.
Given
1, 2, 3, 4, and 5 Customer, and their probability are 0.32, 0.12, 0.23, 0.18, and 0.15.
How to evaluate the probability?
a. [tex]\sum pi = 0.32+0.12+0.23+0.18+0.15 = 1[/tex]
b. Mean number of items = [tex]x*P(x)[/tex]
[tex]\rm x = 1, 2, 3, 4, 5.\\P(x) = 0.32, 0.12, 0.23, 0.18, 0.15[/tex]
[tex]\rm Mean\ number\ of\ items = 1*0.32+2*0.12+3*0.23+4*0.18+5*0.15\\Mean\ number\ of\ items = 2.72[/tex]
c. Standard deviation = [tex]\sqrt{\sum x^{2} *p(x)\ -\ \sum x*p(x)^{2}}[/tex]
[tex]\rm \sum x^{2} *p(x)= 1*0.32 + 4*0.12 +9*0.23 +16*0.18+25*.15\\\sum x^{2} *p(x) = 9.5[/tex]
[tex]\rm \sum x*p(x)^{2} = 1*0.1012 + 2*0.0144 +3*0.0529 +4*0.0324+5*0.0225\\\sum x*p(x)^{2} = 7.4[/tex]
Standard deviation = 1.45
Thus, the probability distribution, mean number, and standard deviation are 1, 2.72, and 1.45.
More about the probability link is given below.
https://brainly.com/question/795909
