Question

According to the Martin Economic Development Council, the average household income in Martin county is $45,725, with a standard deviation of $2,240. Determine the following probabilities. Round solutions to four decimal places, if necessary. Determine the probability that a randomly selected Martin county household has an income greater than o equal to 50,468 . P(x≥$50,468)= Determine the probability that a randomly selected Martin county household has an income between 45,128 and 51,264. P($45,128

Answer 1

To determine the probabilities of different incomes in Martin county, calculate the z-scores and use the standard normal distribution to find the required likelihoods.

Step-by-step explanation:

To find the probability that a randomly selected Martin county household has an income greater than or equal to $50,468, we must first calculate the z-score which is the number of standard deviations away from the mean the value $50,468 is. The formula for the z-score is Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. After finding the z-score, we can use the standard normal distribution table to find the probability that a z-score is greater than or equal to the calculated z-score.

To calculate the probability that a randomly selected household has an income between $45,128 and $51,264, we again calculate the z-scores for both values and then find the probability that the z-score falls between these two values using the standard normal distribution.