The average score of all golfers for a particular course has a mean of 75 and a standard deviation of 4.5. Suppose 81 golfers played the course today. Find the probability that the average score of the 81 golfers exceeded 76. Group of answer choices

The probability that the average score of the 81 golfers exceeded 76

P(x⁻≤ 76) = 0.9772    

Step-by-step explanation:

Step(i):-

Given mean of the Population (μ) = 75

Given standard deviation of the Population (σ) = 4.5

Given size 'n' =81

Let 'X' be the random variable in Normal distribution

Z = 2

Step(ii):-

The probability that the average score of the 81 golfers exceeded 76

P(x⁻≤ 76) = P( Z≤ 2)

               = 1 - P(Z>2)

              = 1 - ( 0.5 - A(2))

              = 0.5 + A(2)

            = 0.5 +0.4772

            = 0.9772

The probability that the average score of the 81 golfers exceeded 76

P(x⁻≤ 76) = 0.9772            

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answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11