Answer:
To calculate the probability that a household in Maryland has an annual income of $100,000 or more, we can use the properties of the normal distribution.
First, we need to standardize the value of $100,000 using the given mean and standard deviation. The standardized value (z-score) is computed using the formula:
z = (x - μ) / σ
Where:
x = desired value (in this case, $100,000)
μ = mean of the distribution (in this case, $75,847)
σ = standard deviation of the distribution (in this case, $33,800)
Plugging in the values:
z = (100000 - 75847) / 33800
z ≈ 0.6728
Next, we need to determine the probability associated with this z-score. We can refer to the z-table or use a statistical calculator to find this value. Looking up the z-score of 0.6728, we find that the corresponding probability is approximately 0.7517.
However, since we want to find the probability of an income of $100,000 or more, we need to calculate the complement of this probability. Thus, the final probability is given by:
1 - 0.7517 ≈ 0.2483
Therefore, the probability that a household in Maryland has an annual income of $100,000 or more is approximately 0.2483, to four decimal places.