According to the Federal Communications Commission, 70% of all U. S. households have vcrs. In a random sample of 15 households, what is the probability that fewer than 13 have vcrs?

The probability  is  

Step-by-step explanation:

From the question we are told that

    The  probability of success is    p = 0.70

     The  sample size is  

Generally the distribution of U.S. households have vcrs follow a binomial distribution given that there are only two outcome (household having vcrs or household not having vcrs )

The probability of failure is mathematically evaluated as

substituting values

The probability that fewer than 13 have vcrs is mathematically represented as

=>    

 Here   means  15 combination 13 and the value is  105 (obtained from calculator)

 Here   means  15 combination 14 and the value is  15 (obtained from calculator)

 Here   means  15 combination 15 and the value is  1 (obtained from calculator)

So

substituting values      

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .