An office supply company conducted a survey before marketing a new paper shredder designed for home use. In the survey, 80% of people used the shredder were satisfied with it. Because of the high acceptance rate, the company decided to make the new shredder. Assume that 80% of all people who use it will be satisfied. On a certain day 7 customers bought the shredder. Let x denote the number of customers in this sample of 7 who will be satisfied with this shredder. Using the binomial probabilities table, obtain the probability distribution of x and fill in the table
x 0 1 2 3 4 5 6 7
p(x)(for each number)

Probability distribution of x

Step-by-step explanation:

Binomial Probability = N c x . (P)^x . (Q)^ n-x

N = Total trials, 7 customers here ; P = Prob of success, 0.80 satisfied here ;    x = No. of success (17) ; Q = Prob of fail, 0.20 not satisfied here

P (x = 1) = 7c1 (0.80)^1 (0.20)^7  = 0.00035

P (x = 2) = 7c2 (0.80)^2 (0.20)^6 = 0.0043

P (x = 3) = 7c3 (0.80)^3 (0.20)^5 = 0.0286

P (x = 4) = 7c4 (0.80)^4 (0.20)^4 = 0.1146

P (x = 5) = 7c5 (0.80)^5 (0.20)^3 = 0.2752

P (x = 6) = 7c6 (0.80)^6 (0.20)^2 = 0.3670

P (x = 7) = 7c7 (0.80)^7 (0.20)^1 = 0.2097

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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step-by-step explanation: