Question

suppose residents in a well-to-do neighborhood pay an average overall tax rate of 25% with a standard deviation of 8%. assume tax rates are normally distributed. what is the probability that the mean tax rate of 16 randomly selected residents is between 20% and 30%.

Answer 1

To find the probability that the mean tax rate of 16 randomly selected residents is between 20% and 30%, you can use the normal distribution. Calculate the standard error of the mean, calculate the z-scores for the lower and upper bounds, and then use a standard normal distribution table or a calculator to find the probability.

Step-by-step explanation:

To find the probability that the mean tax rate of 16 randomly selected residents is between 20% and 30%, we need to use the normal distribution. The average tax rate of the residents in the well-to-do neighborhood follows a normal distribution with a mean of 25% and a standard deviation of 8%.

First, we calculate the standard error of the mean (SE) using the formula: SE = standard deviation / square root of sample size. In this case, SE = 8% / √16 = 2%.

Next, we calculate the z-scores for the lower and upper bounds of the desired range. For a z-score, we use the formula: z = (x - μ) / SE, where x is the desired value, μ is the mean, and SE is the standard error. For the lower bound, z = (20% - 25%) / 2% = -2.5. For the upper bound, z = (30% - 25%) / 2% = 2.5.

Finally, we use a standard normal distribution table or a calculator to find the probability associated with the z-scores. The probability that the mean tax rate of 16 randomly selected residents is between 20% and 30% is the difference between the two probabilities.