A normal population has a mean of 82 and a standard deviation of 9. You select a sample of 55. Use Appendix B.1 for the z-values. Compute the probability that the sample mean is: (Round the z-values to 2 decimal places and the final answers to 4 decimal places.) a. Less than 81. Probability b. Between 81 and 83. Probability c. Between 83 and 86. Probability d. Greater than 86. ProbabilityThe college cafeteria nds that 28% of students will buy a dessert if it is properly advertised. The cafeteria manager is thinking of hiring an arts student to create a poster of a new apple and ice cream dessert. which could then be displayed at the front entrance to the cafeteria during the lunch hours. Normally, 580 students use the cafeteria during lunch time. What is the probability that more than 31% of the students will buy the apple and ice cream dessert? Use Appendix 3.1 for the zvalues. (Round the z-value to 2 decimal places and the final answer to 4 decimal places.) Pro bab il ity |:| A preliminary survey shows that 15% of college students smoke. In a class of 39 students, what is the probability that more than 30% of the students smoke? Use Appendix B.1 for the z-values. (Round the z-value to 2 decimal places and the final answer to 4 decimal places.) Probability