If a random variable follows a normal distribution, what is the probability that the random variable is larger than 1.96 standard deviations below the mean?
A) 95.00%
B) 96.25%
C) 97.50%
D) 98.75%

Question

Quizplus · Accepted Answer

If a random variable follows a normal distribution, we know that approximately 95% of the values lie within 2 standard deviations of the mean. This means that approximately 2.5% of values lie outside of 2 standard deviations below the mean. Since 1.96 standard deviations is less than 2, the probability of the random variable being larger than 1.96 standard deviations below the mean is slightly higher than 2.5%, but less than 5%. The closest option is C, 97.50%.

If a Random Variable Follows a Normal Distribution, What Is