Question

according to money magazine, maryland had the highest mean annual household income of any state in 2018 at $75,847. Assume that annual household income in Maryland follows a normal distribution with a mean of $75,847 and a standard deviation of $33,800. what is the probability that a household in maryland has an annual income of $40,000 or less (to 4 decimals)?

Answer 1

The probability that a household in Maryland has an annual income of $40,000 or less is approximately 0.1635.

Step-by-step explanation:

To find the probability that a household in Maryland has an annual income of $40,000 or less, we need to calculate the z-score and use it to look up the corresponding probability in the standard normal distribution table.

The formula to calculate the z-score is:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

Substituting the given values into the formula:

z = (40,000 - 75,847) / 33,800

= -0.98

Now we can look up the probability corresponding to a z-score of -0.98 in the standard normal distribution table:

The probability is approximately 0.1635.