Answer:
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
[tex]Z = \frac{x-mean}{\frac{S.D}{\sqrt{n} } } = \frac{76-75}{\frac{4.5}{\sqrt{81} } }[/tex]
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
