Final answer:
To calculate the probability of completing the form in more than 12 hours for 36 taxpayers, we need to find the z-score. We would be surprised if the 36 taxpayers finished their Form 1040s in an average of more than 12 hours as the z-score indicates an extremely low probability. For a single taxpayer, we can use the same z-score formula to calculate the probability of taking more than 12 hours.
Step-by-step explanation:
The question asks us to analyze the average time it takes to complete a 1040 tax form based on certain parameters provided by the IRS. We are given that the average time is 3.2 hours with a standard deviation of 15 minutes or 0.25 hours.
To calculate the probability of completing the form in more than 12 hours for 36 taxpayers, we need to find the z-score for that value. The z-score formula is z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. In this case, x = 12, μ = 3.2, and σ = 0.25.
Using the z-score formula, we can calculate the z-score as follows: z = (12 - 3.2) / 0.25 = 32.8
Since the z-score is very high, we would be surprised if the 36 taxpayers finished their Form 1040s in an average of more than 12 hours. This is because the z-score indicates an extremely low probability of this event occurring.
For a single taxpayer, we can use the same z-score formula to calculate the z-score for 12 hours. Since the distribution is normally distributed, we can use the standard normal distribution table or calculator to find the probability associated with this z-score. If the probability is very low, we would be surprised if a single taxpayer took more than 12 hours to complete their Form 1040.