Question

applications with standard normal distribution
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1. the probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal distribution is p%. what can be said with certainty about the probability that the random variable is less than or equal to -z standard deviations from the mean?

○ the probability is less than p%.
○ the probability is equal to p%.
○ the probability is greater than p%.
○ the probability is not equal to p%.

Explanation:

Step1: Recall standard normal symmetry

The standard normal distribution ($N(0,1)$) is symmetric about the mean $\mu=0$. This means $P(X \geq z) = P(X \leq -z)$ for any real number $z$.

Step2: Match given probability to symmetric case

We are told $P(X \geq z) = p\%$. By symmetry, $P(X \leq -z)$ must equal this same value.

Answer:

The probability is equal to $p\%$.