MY NOTES An article discussing a rise in the proportion of Americans with tattoos over a seven year period describes a survey of 1 009 adult Americans Suppose that it is reasonable to regard this sample as a random sample from the population of adult Americans Of the survey participants 289 reported that they had at least one tattoo a Suppose you are interested in learning about the value of p the proportion of all adult Americans who have at least one tattoo This proportion can be estimated using the sample proportion p What is the value of p for this sample Round your answer to four decimal places pa PRACTICE ANOTHER b Based on what you know about the sampling distribution of p is it reasonable to think that this estimate is within 0 05 of the actual value of the population proportion Explain why or why not Hint See Example 8 4 Round your answer to four decimal places Need Help We know the sampling distribution of p will be centered at the Select sampling distribution is approximately normal the following fact The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center and our standard deviation is less than 0 05 We cannot make use of the Empirical Rule since our sampling distribution isn t mound shaped and symmetric The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center but two standard deviations is greater than 0 05 The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center and two standard deviations is less than 0 05 The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center but our standard deviation is greater than 0 05 Read It and the standard deviation of this distribution can be estimated as So we can In addition the B say our value of p is likely to be within 0 05 of the actual value because of