the probability that a random variable is greater than or equal to z standard deviations from the mean in a…

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?\n\nthe probability is less than p%.\nthe probability is equal to p%.\nthe probability is greater than p%.\nthe probability is not equal to p%.

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?\n\nthe probability is less than p%.\nthe probability is equal to p%.\nthe probability is greater than p%.\nthe probability is not equal to p%.

Answer

Answer:

The probability is equal to $p%$.

Explanation:

Step1: Recall normal - distribution property

The standard normal distribution $N(0, 1)$ is symmetric about the mean $\mu = 0$.

Step2: Analyze the two regions

The region of values greater than or equal to $z$ standard - deviations from the mean ($x\geq\mu + z\sigma$ where $\mu = 0,\sigma = 1$) and the region of values less than or equal to $-z$ standard - deviations from the mean ($x\leq\mu - z\sigma$) are symmetric about the mean. So, if the probability that a random variable is greater than or equal to $z$ standard deviations from the mean is $p%$, then the probability that the random variable is less than or equal to $-z$ standard deviations from the mean is also $p%$.