Question

CRA CDs Inc. wants the mean lengths of the “cuts” on a CD to be 170 seconds (2 minutes and 50 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows a normal distribution with a standard deviation of nine seconds. Suppose that we select a sample of 16 cuts from various CDs sold by CRA CDs Inc. Use Appendix B.1 for the z-values.

a. What can we say about the shape of the distribution of the sample mean?

Sample mean is normal

b. What is the standard error of the mean? (Round the final answer to 2 decimal places.)

Standard error of the mean 2.25 seconds.

c. What percentage of the sample means will be greater than 174 seconds? (Round the final answer to 2 decimal places.)

Sample means             %

d. What percentage of the sample means will be greater than 166 seconds? (Round the final answer to 2 decimal places.)

Sample means             %

e. What percentage of the sample means will be greater than 166 but less than 174 seconds? (Round the final answer to 2 decimal places.)

Appendix B.1 Areas under the Normal Curve Examale Iz196. then P0 to z)0.4750 04750 96 0.00 0.09 0.01 0.08 0.02 0,07 0.03 0.06 0.04 0.05 0.0 0.0000 0.0359 0.0040 0.0319 0.0279 00080 0.0239 0.1 0.0398 0517 0.0753 0.0438 0.0714 00478 0.0675 0.0636 0.2 0.0793 0.1141 0.1103 0.0832 0,1064 0.0871 ,1026 0.0010 0.0987 0.0948 0.2 0.1517 0.1179 0.1480 0.1217 0.1443 0.1255 0.1406 0.1208 0.1388 0.1331 0.4 0.1879 0.1564 0.1591 0.1844 0.1808 0.1628 0.1664 0.1772 0.1700 0.1736 0.2224 0.5 0.1915 0 2190 0.1950 0.2123 0.2157 0.1985 0.2019 0.2064 0,2088 02517 0.2549 0.6 0.2257 0.229 0.2480 0,2324 0.2464 0.2357 0.2422 0.238 0.2852 0.7 0.2580 0,2823 0.2611 02794 0.2642 0.2764 0.2673 0.2734 0.2704 0.3133 0.8 03106 0.2881 0.3078 0.2910 0,2939 0.2967 0.3023 0.3051 0.2995 0.3889 0.9 0.3159 0,8365 0.3186 0.3340 0.3212 D.3289 0.3316 0.3238 0.3264 0.35 0.3621 0,3509 1. 0,3413 0.3677 0.3438 0.3461 0.3531 0.3485 0.3508 0.383 0.3810 11 0.3643 0.3665 0.3770 0.3790 0.3686 0.3708 0,3749 0.3729 0.3997 0.4015 1.3 0.3849 0.3980 0.3869 0.3888 0.307 0.3944 03962 0.3925 0.4177 0.4147 0.4162 1.2 0.4032 04049 0.4066 0.4115 0.4131 11082 4099 0.4319 0.4192 0.4207 0.4279 4292 0.4306 14 .1222 0.4236 0.4251 0.1265 0.4418 0.4429 0.4441 15 0.4332 0.4345 n4357 0.4370 0.4382 0.4394 0.4406 0.4484 0.4516 0.4525 0.4535 0.4545 0.4452 0.4463 0.4474 0.4195 04505 0.4616 0.4626 0.4633 1.' 0.4554 04564 0.4573 0.4582 0.4591 0.4599 0.4608 0464 0.4666 0.4664 0.467 0,4678 0.4686 0.4693 0.4699 0.4706 18 0.4041 04738 0.4744 04760 0.4756 0.4761 0.4767 1.9 0.4713 0.4719 0.4726 1.4732 0.4817 0.4778 0.4783 0.4788 0.4783 0.4798 1.4803 0.4808 0.1812 2.0 0.4772 0.4850 0.4842 0.4854 0.4857 0.4826 0.4830 0.4834 0.4838 0.4846 2. 0.4821 0.4868 0.4871 0.4875 0,4878 0.4881 0.4884 0,4887 0.4890 0.4861 0.4864 .4901 0.4904 0.4906 0.4909 0.4011 0.4913 0.4916 0.4893 0.4896 0.4898 2.3 0.4927 0.4929 0.4931 0.4932 04936 0.4920 0.4922 0.4925 0.4934 2.4 0.4918 0.4940 0.4941 0.4943 0,4945 0.4946 0.4948 0.4949 04951 0.4952 2 0.4938 0.4955 0.4956 0.4967 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964 2.6 04953 0.4968 04969 04970 0.4971 0.4972 0.4973 0.4974 27 0.4965 0.4966 047 04980 0.4977 0.4978 0.4970 0.4979 04981 0.4976 0.4976 0.1977 2.8 0.4974 0.4084 0.4084 0.4985 0.4985 0.4986 0.4986 0.4981 0.4982 0.4982 0.1983 2.9 04988 0.4989 0.4989 0.4989 0.4987 0.4987 0.4988 0.4990 04990 3.0 04987 AP-55

Answer 1

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