K The data in the table represent a possible starting lineup for a basketball team. Use the data to answer questions (a) through (e). (Assume that sampling is without replacement.) Player Position Height (in.) A Center 83 BCDE Guard 70 Forward 80 Guard 76 Forward 80 a. Find the population mean height of the five players. H=77.8 inch(es) (Type an integer or a decimal. Do not round.) b. For samples of size 3, construct a table of all possible samples and their sample means. Sample Heights Sample Heights A, B, C 83, 70, 80 A, D, E 83, 76, 80 A, B, D 83, 70, 76 B, C, D 70, 80 76 8076 A, B, E 83, 70, 80 B, C, E 70, 80, 80 A, C, D 83, 80, 76 B, D, E 70, 76, 80 A, C, E 83, 80, 80 C, D, E 80, 76, 80 (Round to two decimal places as needed.) IX c. Draw a dotplot for the sampling distribution of the sample mean for samples of size 3. Choose the correct dotplot below. O A. O B. 74 C. 175 75 76 77 78 79 TR 75 76 77 78 79 80 80 - 80 81 82 G O D. 75 76 77 78 79 80 81 82 G . 78 81 82 G LV r S . 74 75 76 77 78 79 80 81 -2 82 d. For a random sample of size 3, what is the chance that the sample mean will equal the population mean? (Type an integer or a decimal. Do not round.) e. For a random sample of size 3, obtain the probability that the sampling error made in estimating the population mean by the sample mean will be 2 inches or less; that is, determine the probability that x will be within 2 inches of . Interpret your result in terms of percentages. The probability is The probability is 0 (Type an integer or a decimal. Do not round.) Interpret the result in terms of percentages. If a random sample of two heights is taken, there is a % chance that the mean of the population selected will be within 2 inches of the population mean. (Type an integer or a decimal. Do not round.)