The Greenline Taxi Company in New York City keeps careful records of items left behind by riders. Most items are claimed, but many remain in a lost-and-found area at the company’s headquarters....

The Greenline Taxi Company in New York City keeps careful records of items left behind by riders. Most items are claimed, but many remain in a lost-and-found area at the company’s headquarters. Records indicate that the proportion of riders who leave an item in a taxi is 0.12. Suppose a random sample of 250 riders is obtained.

 a. Find the sampling distribution of the sample proportion of riders who leave an item behind. Carefully sketch the probability density function.

b. What is the probability that the sample proportion of riders who leave an item behind is more than 0.15?

c. What is the probability that the sample proportion of riders who leave an item behind is between 0.11 and 0.115?

d. Some people speculate that in bad economic times, riders (and people in general) are more careful with their belongings. Suppose this sample was obtained during a recession, and the sample proportion of riders who left an item behind was 0.09. Is there any evidence to suggest that the true proportion is less than 0.12?