Answer:
The probability that a value in the data set is greater than or equal to 162
P(X≥162) = 0.0207
<u>Step-by-step explanation:</u>
<u>Step(i)</u>:-
Given mean of the Population = 115
Given standard deviation of the Population = 23
Let 'x' be the random variable of normal distribution
Let x = 162
z = 2.043
<u><em>Step(ii)</em></u>:-
<em>The probability that a value in the data set is greater than or equal to 162</em>
<em>P(X>x) = P(Z>z) = P(Z> 2.043)</em>
P(X≥162) = P(Z≥2.043) = 1-P(Z≤ 2.043)
= 1- ( 0.5 +A(2.043)
= 1-0.5 -A(2.043)
= 0.5 - 0.4793
= 0.0207
<u><em>Final answer</em></u>:-
<em>The probability that a value in the data set is greater than or equal to 162</em>
<em>P(X≥162) = 0.0207</em>
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