Question

O 3/5 points | Previous Answers PODStat6 7.XP003. Suppose that for a given computer salesperson, the probability distribution of x the number of systems sold in one month is given by the following table. 1 3 4 x 5 6 7 8 P(x) 0.06 0.10 0.11 0.30 0.29 0.12 0.01 0.01 (a) Find the mean value of x (the mean number of systems sold). mean 4.11 (b) Find the variance and standard deviation of x. (Round the answers to four decimal places.) variance 21.834 standard deviation 2.223 (c) What is the probability that the number of systems sold is within 1 standard deviation of its mean value? Pίμ- σ x< μ + σ)- 07 (d) What is the probability that the number of systems sold is more than 2 standard deviations from the mean? P(x < -2a or x> u+20)- 0.08 You may need to use the appropriate table in Appendix A to answer this question. Need Help? Talk to a Tutor Read It

Answer 1

Solution: Given that

x : 1,2,3,4,5,6,7,8
p(x) : 0.06,0.10,0.11,0.30,0.29,0.12,0.01,0.01

(b) Variance = 2.0579

  
standard deviation = 1.4345

Explanation In order to find the variance (o2 of the given distribution, we will use the following formula: In this example: 411 100 on how to find mean) (use "Find the Mean" option in this calculator for the step-by-step explanation Now we will find the sum: 3 3 +42. +52. 10 29 +62 100 3 +72 25 1 11 Xp<x) = 1? . +22 +32 +82. 100 . 10 100 100 50 379 20 Putting all together we have: 379 20579 411 2= pz)= 20 100 10000

Explanation In order to find the standard deviation of the given distribution, we will use the following formula: In this example: 411 100 (use "Find the Mean" option in this calculator for the step-by-step explanation on haw to find mean) Now we will find the sum: 3 12 50 29 1 11 +42 100 1 1 Ft22 +32 10 +52 10 +82 100 +62. +72 . 25 100 100 379 20 Putting all together we have: 379 20579 411 1,4345 20 10000 100