Exploring the Central Limit Theorem.. and how to know when to use it... 1. Fat Content in Hot Dogs An independent testing organiza pork hotdogs whose fat content ( mean of 18 grams, and standard center and spread of the samplin would result from each sample b a. X= individual fat content of one randomly selected pork hotdog X~ is distributed according to a _distribution with / =_ O= b. A random sample of 2 pork hotdogs is selected. = average fat content (per hotdog) when a sample of 2 hotdogs is averaged. ~ is distributed according to a distribution with / =_ 0 = c. A random sample of 4 pork hotdogs is selected. = average fat content (per hotdog) when a sample of 4 hotdogs is averaged. ~ is distributed according to a distribution with / =_ 0 = d. A random sample of 16 pork hotdogs is selected. = average fat content (per hotdog) when a sample of 16 hotdogs is averaged. ~ is distributed according to a distribution with / =_ e. Name the sample size for each of the random samples above: In part(b): n = In part(c): n = In part(d): n = Are these sample sizes considered large samples or small samples? Are the distributions in (b)-(d) "normally distributed"? Explain how you know. (hint: use property 3a or 3b on the previous page to justify your answer)2. Bluethroat Song Duration Male bluethroats have a complex to attract female birds. Let x dent selected song [in seconds] from a research on bluethroat song repo seconds and the standard deviati seconds. The authors also noted 1 not normal. a. Let = average song duration [in seconds) for a sample of36 male bluethroat songs. Is this distribution ofthe sample mean song duration "normally distributed\"? Explain how you know. (hint: use property 3a or 3b to justify your answer) b. Find the probability that a sample of36 male bluethroat songs will have a mean duration greater than 12 seconds. Draw, label, and shade a graph to illustrate your result. = average song duration [in seconds} for the sample of36 male bluethroat songs. ~ is distributed according to a distribution with ,u = . a' = Draw and label the distribution of for this problem: Find P[ > 12) =