To find the value of [tex]\( P(z \geq a) \)[/tex] for a standard normal distribution, we need to use the properties of the cumulative distribution function (CDF) and the complementary probability.
Given:
[tex]\[ P(z \leq a) = 0.7116 \][/tex]
The probability [tex]\( P(z \leq a) \)[/tex] represents the area under the standard normal curve to the left of [tex]\( a \)[/tex]. The total area under the standard normal distribution curve is 1.
The complementary probability [tex]\( P(z \geq a) \)[/tex] represents the area under the standard normal curve to the right of [tex]\( a \)[/tex]. We can find this complementary probability by subtracting [tex]\( P(z \leq a) \)[/tex] from 1.
[tex]\[ P(z \geq a) = 1 - P(z \leq a) \][/tex]
Substituting the given value:
[tex]\[ P(z \geq a) = 1 - 0.7116 \][/tex]
[tex]\[ P(z \geq a) = 0.2884 \][/tex]
Therefore, the value of [tex]\( P(z \geq a) \)[/tex] is:
[tex]\[ 0.2884 \][/tex]
So the correct answer is:
[tex]\[ \boxed{0.2884} \][/tex]
