When treated with an antibiotic, 94% of all the dolphins are cured of an ear infection. if 8 dolphins are treated, find the probability that exactly 4 are cured.

0.071%

Step-by-step explanation:

The probability of success is constant, and each dolphin is independent, so this is an example of a binomial distribution.

P = nCr p^r q^(n-r)

where P is the probability of r number of successes out of n number of trials, p is the probability of success, and q is probability of failure (1-p).

Given: n = 8, r = 4, p = 0.94, q = 0.06:

P = ₈C₄ (0.94)⁴ (0.06)⁸⁻⁴

P = 70 (0.94)⁴ (0.06)⁴

P ≈ 0.071%

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.