A report claimed that 20% of respondents subscribe to the “5-second rule.” That is, they would eat a piece of food that fell onto the kitchen floor if it was picked up within 5 seconds. Assume this figure is accurate for the population of U. S. adults. Let = the proportion of people who subscribe to the 5-second rule in an SRS of size 80 from this population. 1. Calculate the mean and the standard deviation of the sampling distribution of .
2. Interpret the standard deviation from part (a).
3. Justify that it is appropriate to use a normal distribution to model the sampling distribution of .
4. In an SRS of size 80, only 10% subscribed to the 5-second rule. Does this result provide convincing evidence that the proportion of all U. S. adults who subscribe to the 5-second rule is less than 0.20? Calculate P( ≤ 0.10) and use this result to support your answer.