44. A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 50

adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases?

(a) 20% of all adult Americans support the changes

(b) 25% of all adult Americans support the changes

20. The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips.

(a) What is the probability that a randomly selected bag contains between 1000 and 1500 chocolate chips?

(b) What is the probability that a randomly selected bag contains fewer than 1000 chocolate chips?

(c) What proportion of bags contains more than 1175 chocolate chips?

(d) What is the percentile rank of a bag that contains 1025 chocolate chips?