The fuel consumption, in miles per gallon, of all cars of a particular model has a mean of 29 and a standard deviation of 3. The population distribution can be assumed to be normal. A random sample of these cars is taken. Complete parts a and b below. El Click on the inn to view the standard normal table a. Find the probability that the sample mean fuel consumption will be fewer than 28 miles per gallon if samples of 1, 4, and 9 are taken. The probability for a sample of 1 observation is (Round to four decimal places as needed.) The probability for a sample of 4 observations is (Round to four decimal places as needed.) The probability for a sample of 9 observations is (Round to four decimal places as needed.) b. Explain why the three answers in part (a) differ in the way they do. Draw a graph to illustrate your reasoning. As the sample size increases, the mean of the sampling distribution of X and the standard deviation Therefore, the sample means tend to the population mean. Since 28 is less than the population mean, the portion of the sampling distribution of X that represents sample means fewer than 28 as the sample size increases. Which graph shows the correct relationship between the sampling distributions of X for two samples of n, and n2 observations, where n2 is larger than n, and x is a sample mean less than the population mean? O A. O B. O c. OD. Ap Ap Ap X I Ap X -X I n2 n2 n1 n1 n2 n1 n2 n1 x X X Xel consumption will be fewer than 28 miles per gallon if samples of 1, 4, a s is is is differ in the way they do. Draw a graph to illustrate your reasoning. the sampling distribution of X and the standard deviation he population mean. Since 28 i mean, the portion of the 28 S ip between the sampling distribu increases of n, and n2 observation population mean? stays the same B. decreases OD. AP X AP X n2 m1 n1 n2 Q n1 X Xel consumption will be fewer than 28 miles per gallon if samples of 1, 4, a s is is is differ in the way they do. Draw a graph to illustrate your reasoning. the sampling distribution of X and the standard deviation he population mean. Since 28 i mean, the portion of the 28 S ip between the sampling distribu increases of n, and n2 observation population mean? stays the same B. decreases OD. AP X AP X n2 m1 n1 n2 Q n1 X Xtil!) ____ rill be fewer than 28 miles per gallon if samples of 1, 4, and 9 are taken. they do. Draw a graph to illustrate your reasoning. ribution of i 71 and the standard deviation Therefore. the an. Since 28 is less than the population mean, the portion 0 f)? 1' as the sample size increases. impling distributions of i for two samples of n1 and n2 obse increases. than stays the same. 0 l decreases. (\"x ' -.' 'i .. . - \\_/' \\'jV . ['11 Q r'\"\\ n .-'-' x 'r " 3' 2 x ' 2' '. I ('75) __ __ ind the probability that the sample mean fuel consumption will be fewer than 28 miles per gallon if sample: a probability for a sample of 1 observation is [J Jund to four decimal places as needed.) e probability for a sample of 4 observations is I} ound to four decimal places as needed.) is probability for a sample of 9 observations is [j tound to four decimal places as needed.) . Explain why the three answers in part (a) differ in the way they do. Draw a graph to illustrate your reasoning. is the sample size increases. the mean of the sampling distribution of )7 and the standard deviatir iample means tend to ' {w the population mean. Since 28 is less than the population mean, the portioi :V as the sample size increases. hat represents sam pie Which graph shows the an the sampling distributions of X for two samples of n1 and n2 obs n1 and i is a sample rn get closer to "n mean? get farther from ' O A. . O c. O : n1 1'12 Q (34:) 1e probabllity that the sample mean fuel consumption will be fewer than 28 miles per gallon if samples of 1 :ability for a sample of 1 observation is [1.] to four decimal places as needed.) ,I bability for a sample of 4 observations is [j to tour decimal places as needed.) abability for a sample of 9 observations is r] l to four decimal places as needed.) .ain why the three answers in part (a) differ in the way they do. Draw a graph to illustrate your reasoning. sample size increases. the mean of the sampling distribution of )_