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Annual household income in Maryland follows a normal distribution with a mean of 75847 and standard deviation of 33800. What is the probability that a household has an annual income of 100000 or more to four decimals

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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.

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