Answer :
Given the problem, we are dealing with a standard normal distribution, which is symmetric about the mean (0). The probabilities for standard normal distribution values are given using the Z-table or standard normal distribution table.
We know the probability [tex]\( P(z \leq a) \)[/tex]:
[tex]\[ P(z \leq a) = 0.7116 \][/tex]
To find the probability [tex]\( P(z \geq a) \)[/tex], we use the fact that the total probability for all possible outcomes in a distribution is 1. Therefore, [tex]\( P(z \geq a) \)[/tex] is the complement of [tex]\( P(z \leq a) \)[/tex].
The complement rule states:
[tex]\[ P(z \geq a) = 1 - P(z \leq a) \][/tex]
Substitute the given probability into the equation:
[tex]\[ P(z \geq a) = 1 - 0.7116 \][/tex]
[tex]\[ P(z \geq a) = 0.2884 \][/tex]
So, the value of [tex]\( P(z \geq a) \)[/tex] is:
[tex]\[ \boxed{0.2884} \][/tex]
We know the probability [tex]\( P(z \leq a) \)[/tex]:
[tex]\[ P(z \leq a) = 0.7116 \][/tex]
To find the probability [tex]\( P(z \geq a) \)[/tex], we use the fact that the total probability for all possible outcomes in a distribution is 1. Therefore, [tex]\( P(z \geq a) \)[/tex] is the complement of [tex]\( P(z \leq a) \)[/tex].
The complement rule states:
[tex]\[ P(z \geq a) = 1 - P(z \leq a) \][/tex]
Substitute the given probability into the equation:
[tex]\[ P(z \geq a) = 1 - 0.7116 \][/tex]
[tex]\[ P(z \geq a) = 0.2884 \][/tex]
So, the value of [tex]\( P(z \geq a) \)[/tex] is:
[tex]\[ \boxed{0.2884} \][/tex]
