6.8k views
1 vote
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

1 Answer

7 votes

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.

User Hasan Zahran
by
7.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories