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Exercise 13-16: Candy Colors 1-13, 2-19, 13-1, 13-2, 13-15, 13-16, 13-20, 16-5, 16-22, 24-15, 24-16 Reconsider the previous exercise. Now suppose you take simple random samples of size n = 175 from the population of Reese's Pieces candies, still assuming that 45% of this population is orange (= .45). vs. d.

a. According to the Central Limit Theorem, how will the sample proportion of orange candies vary from sample to sample? Describe not only the shape of the distribution but also its mean and standard deviation. What has changed about this sampling distribution from when the sample size was 75?

b. Sketch this sampling distribution, and shade the area corresponding to the probability that a sample proportion of orange candies will be less than .4 (with a sample size of 175). By looking at this area, guess the value of the probability.

c. Calculate the probability that (with a sample size of 175) a sample proportion of orange candies will be less than .4.

d. How does this probability differ from the probability when the sample size is 75? Explain why this result makes sense. not

e. Calculate the probability that a sample proportion of orange candies (using a sample size of 175) falls between .35 and 55 (within +.10 of .45).

f. How does the probability in part e differ from when the sample size is 75? Explain why this result makes sense.