According to a recent survey, about 33% of Americans polled said that they would likely purchase reusable cloth bags for groceries in order to reduce plastic waste. Suppose 45 shoppers are interviewed a local supermarket.
a. Describe the sampling distribution for the sample proportion by naming the model and determining its mean and standard deviation.
b. What is the probability that no more than 28% of shoppers say that they are likely to purchase reusable cloth bags for groceries?
c. What is the probability that between 28% and 38% of shoppers say that they are likely to purchase reusable cloth bags for groceries?
d. A small business ships specialty homemade candies to anywhere in the world. Past records indicate that orders weigh an average of 118 grams with a standard deviation of 14 grams. Suppose a random sample of 50 current orders is selected and each weighed. What is the probability that the sample mean is greater than 120 grams?