Question

for a standard normal distribution, if $p(z \leq a) = 0.7116$, what is the value of $p(z \geq a)$?
\bigcirc\\ 0.2116
\bigcirc\\ 0.2884
\bigcirc\\ 0.7116
\bigcirc\\ 0.7884

Explanation:

Step1: Recall the property of standard normal distribution

In a standard normal distribution, the total probability is 1, and the events \( z \leq a \) and \( z \geq a \) are complementary. So we use the formula \( P(z \geq a)=1 - P(z \leq a) \).

Step2: Substitute the given value

We know that \( P(z \leq a) = 0.7116 \), so substitute this value into the formula: \( P(z \geq a)=1 - 0.7116 \).

Step3: Calculate the result

Calculate \( 1 - 0.7116 = 0.2884 \).

Answer:

0.2884 (corresponding to the option "0.2884")