Answer:
The probability that a value in the data set is greater than or equal to 162
P(X≥162) = 0.0207
Explanation:
Step(i):-
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
Step(ii):-
The probability that a value in the data set is greater than or equal to 162
P(X>x) = P(Z>z) = P(Z> 2.043)
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
Final answer:-
The probability that a value in the data set is greater than or equal to 162
P(X≥162) = 0.0207