Answer Questions 1-8, and 11-16.

for all questions, draw and shade the curves, if applicable

Graphical Analysis In Exercises 11 and 12, the graph of a population distribution is shown with its mean and standard deviation. Assume that a sample size of 100 is drawn from each population. Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means for each graph. Explain your reasoning. 11. The waiting time (in seconds) at a traffic signal during a red light P(x) 0.035 - " = 11.9 0.030 -+ 0.025 0.020 + Relative frequency 0.015 want my and 0.010 -+ M = 16.5 0.005 10 20 30 40 50 Time (in seconds) in(b) P(x) (c) P(x) OF = 11.9 0.035 - 0- = 11.9 of = 1.19 H = 16.5 0.030-+ 0.025 - H = 16.5 0.3 Relative frequency gonub vel esilt senor elative frequency _ 0.020- Relative frequency 0.2+ 0.015- U-= 16.5 0.010 0.1 + 2 0.005- -10 0 10 20 30 40 + 4+ - X 10 20 30 40 50 Time (in seconds) 10 20 30 40 Time (in seconds) Time (in seconds) moby 12. The annual snowfall (in feet) for a central New York State county P(x ) 10o spiel s Is esovoin Relative frequency Inweb udmelb yHerson a in abauog C.BE To to nsom sus bas fro Islogog Snowfall (in feet) d slab foe to noll (a) P (X ) (b) 10-=2.3 1-= 5.8 OF =0.23 (c .8+ 2.0 + 0= =2.3 Be mobuy analleg 0.12 1.5 - 1.6 - My = 5.8 quite doso to risem Relative frequency 1.2 0.08 1.2 requency 6 0.9- H- = 5.8 Frequency 0.8 0.04 5 0.6- quad JedW .OF bus ES 0.3 0.4+ encom olgine to no tusdia 2 6 8 10 2 4 - X 6 8 10 -2 0 2 4 6 8 10 12 Snowfall (in feet) Snowfall (in feet) Snowfall (in feet) Finding Probabilities In Exercises 13-16, the population mean and standard deviation are given. Find the required probability and determine whether the given sample mean would be considered unusual. If convenient, use technology to find the probability. 13. For a sample of n = 36, find the probability of a sample mean being less than 12.2 if u = 12 and o = 0.95. 14. For a sample of n = 100, find the probability of a sample mean being greater than 12.2 if u = 12 and o = 0.95. 15. For a sample of n = 75, find the probability of a sample mean being greater than 221 if u = 220 and o = 3.9. 16. For a sample of n = 36, find the probability of a sample mean being less than 12,750 or greater than 12,753 if u = 12,750 and o = 1.7. Using and Interpreting Concepts Using the Central Limit Theorem In Exercises 17-22, use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution.I Building Basic Skills and Vocabulary In Exercises [4, a population has a mean 1.1. = 100 and a standard damn-0 a = 15. Find the mean and standard deviation of a sampling distribution n sample means with the given sample size n. of 1.n=50 2.n=100 3. n = 250 4. n = 1000 True or False? In Exercises 58, determine whether the statement is true or false. If it is false, rewrite it as a true statement. 5. As the size of a sample increases, the mean of the distribution of sample means increases. 6. As the size of a sample increases, the standard deviation of the distribution of sample means increases. 7. A sampling distribution is normal only if the population is normal. 8. If the size of a sample is at least 30, you can use z-scores to determine the probability that a sample mean falls in a given interval of the samng distribution