Question

Suppose x is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that x equals 19.62 is _____.

Answer 1

Answer:

The probability that x equals 19.62 is 0

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In the normal probability distribution, the probability of an exact value, that is, P(X = x) is 0. Thus, the probability that x equals 19.62 is 0