The entries in the table are the probabilities that a random variable having the standard normal distribution takes on a value between 0 and z; they are equal to the area under the curve shaded in the figure. AREAS UNDER THE STANDARD NORMAL CURVE Second Decimal Place in z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359 .0 .1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753 .1 .2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141 .2 .3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517 .3 .4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879 .4 .5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224 .5 .6 .2257 .2291 2324 .2357 .2389 .2422 .2454 .2486 .2517 .2549 .6 .2580 .2611 .2881 .2910 .2939 .2967 .2995 .7 2642 2673 2704 .2704 .2734 .2764 .2794 .2823 .2852 .7 .8 .3023 3051 .3078 3106 .3133 .8 .9 .3159 .3186 .3212 .3238 .3264 3289 .3315 3340 .3365 .3389 .9 .3413 .3438 .3461 .3485 3508 .3531 .3554 .3577 .3599 .3621 1.0 .3749 3770 .3790 .3810 .3830 1.1 .3849 .3869 .3888 3907 .3925 3944 3962 3980 3997 .4015 1.2 .4032 .4049 4066 .4082 .4090 .4115 .4131 .4147 4162 .4177 1.3 4192 .4207 4222 .4236 .4251 .4265 .4279 .4292 .4306 4319 1.4 1.0 1.1 .3643 .3665 3686 3708 1.2 1.3 1.4 .4332 .4345 4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441 1.5 .4452 .4463 4474 4484 .4495 .4505 .4515 .4525 .4535 .4545 1.6 .4554 .4564 4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633 1.7 .4641 4649 4656 .4664 .4671 .4678 .4686 .4693 .4699 4706 1.8 4713 .4719 4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767 1.9 1.5 1.6 1.7 1.8 1.9 .4772 .4778 .4783 .4788 .4793 .4798 4803 4808 .4812 .4817 2.0 .4821 .4826 4830 .4834 .4838 .4842 .4846 .4850 4854 .4857 2.1 .4861 .4864 4868 .4871 .4875 .4878 .4881 .4884 .4887 4890 2.2 .4893 .4896 4898 .4901 4904 .4906 .4909 .4991 .4913 4916 2.3 .4918 .4920 4922 4925 .4927 .4929 4931 .4932 4934 .4936 2.4 2.0 2.1 2.2 2.3 2.4 .4949 .4951 4952 2.5 .4953 .4955 4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964 2.6 .4965 .4966 4967 4968 4969 .4970 4971 .4972 4973 .4974 2.7 .4974 .4975 4976 4977 4977 .4978 4979 .4979 4980 .4981 2.8 .4981 .4982 4982 .4983 .4984 .4984 4985 .4985 4986 .4986 2.9 2.5 .4938 .4940 4941 .4943 .4945 .4946 .4948 2.6 2.7 2.8 2.9 .4987 .4987 4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990 3.0 .4990 .4991 .4991 .4991 .4992 .4992 .4992 .4992 4993 .4993 3.1 .4993 .4993 .4994 .4994 4994 .4994 4994 .4995 .4995 .4995 3.2 .4995 .4995 4995 4996 .4996 .4996 4996 .4996 4996 .4997 3.3 .4997 .4997 4997 .4997 .4997 .4997 4997 .4997 4997 .4998 3.4 3.0 3.1 3.2 3.3 3.4 .4998 .4998 .4998 .4998 .4998 .4998 .4998 .4998 4998 .4998 3.5 .4998 .4998 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 3.6 3.5 3.6 3.7 .4999 .4999 4999 4999 4999 .4999 4999 4999 4999 .4999 3.7 3.8 .4999 .4999 4999 .4999 .4999 .4999 4999 .4999 4999 .4999 3.8 3.9 .5000 3.9 For z 2 3.90, the areas are .5000 to four decimal places.

A population of values has a normal distribution with M=153.9 and O=82.9 You intend to draw a random sample of size n=115. A). Find P86, which is the score separating the bottom 86% scores from the top 14% scores. P86 (for single values) =__________ B). Find P86, which is the mean separating the bottom 86% means from the top 14% means. P86 (for sample means) =_________

Find the area under the standard normal curve to the right of z = 2.04 z= 1.09 Genetics: Pea plants contain two genes for seed color, each of which may be Y (for yellow seeds) or G (for green seeds). Plants that contain one of each type of gene are called heterozygous. According to the Mendelian theory of genetics, if two heterozygous plants are crossed, each of their offspring will have probability 0.75 of having yellow seeds and probability 0.25 of having green seeds. One hundred such offspring are produced. Approximate the probability that more than 30 have green seeds.

Suppose that a random variable Z has a standard normal distribution. Use a standard normal table such as this one to determine the probability that Z is between −1.33 and 0.67. Give your answer in decimal form, precise to at least three decimal places. P(−1.33<Z<0.67)=