Question

According to Money magazine, Maryland had the highest median annual household income of any state in at (Time website). Assume that annual household income in Maryland follows a normal distribution with a median of and standard deviation of . a. What is the probability that a household in Maryland has an annual income of or more (to 4 decimals)

Answer 1

Answer:

The probability that a household in Maryland has an annual income of X or more is 1 subtracted by the p-value of $Z = \frac{X - \mu}{\sigma}$, in which $\mu$ is the mean income and $\sigma$ is the standard deviation of incomes.

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 this question:

Mean $\mu$, standard deviation $\sigma$

What is the probability that a household in Maryland has an annual income of X or more?

The probability that a household in Maryland has an annual income of X or more is 1 subtracted by the p-value of $Z = \frac{X - \mu}{\sigma}$, in which $\mu$ is the mean income and $\sigma$ is the standard deviation of incomes.