Question

According to Money magazine, Maryland had the highest mean annual household income of any state in 2018 at $75,847 (Time.com website). Assume that annual household income in Maryland follows a normal distribution with a mean of $75,847 and standard deviation of $33,800.

a. What is the probability that a household in Maryland has an annual income of $100,000 or more (to 4 decimals)?

Answer 1

To find the probability that a household in Maryland has an annual income of $100,000 or more, we can use the z-score formula. The probability is 0.2389.

Step-by-step explanation:

To find the probability that a household in Maryland has an annual income of $100,000 or more, we can use the z-score formula.

First, we need to calculate the z-score:

z = (x - mean) / standard deviation

where x is the value of the income, mean is the mean annual household income in Maryland, and standard deviation is the standard deviation of annual household income in Maryland.

Plugging in the values:

z = (100,000 - 75,847) / 33,800 = 0.7152

Next, we need to find the area under the standard normal distribution curve to the right of this z-score. We can use a standard normal distribution table or a calculator to find this area.

The probability can be calculated as 1 - the area to the left of the z-score:

P(X ≥ 100,000) = 1 - P(X ≤ 100,000)

Using the standard normal distribution table or a calculator, we find that the area to the left of the z-score 0.7152 is 0.7611.

Therefore, the probability that a household in Maryland has an annual income of $100,000 or more is:

P(X ≥ 100,000) = 1 - 0.7611 = 0.2389 (rounded to 4 decimals).