A data set is normally distributed with a mean of 115 and a standard deviation of 23. What is the probability that a value in the data set is greater than or equal to 162?
The probability is about __

The probability that a value in the data set is greater than or equal to 162

P(X≥162) = 0.0207

Step-by-step 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

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step-by-step explanation: