Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability that

a. Z is between -1.23 and 1.64?

b. Z is less than -1.27 or greater than 1.74?

c. For normal data with values symmetrically distributed around the mean, find the Z values that contain 95% of the data.

d. Find the value of Z such that the area to the right is 2.5% of the total area under the normal curve.

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TABLE E.2 The Cumulative Standardized Normal Distribution Entry represents area under the cumulative standardized normal distribution from -0 to Z ZO Cumulative Probabilities Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -6.0 0.000000001 -5.5 0.000000019 -5.0 0.000000287 -4.5 0.000003398 -4.0 0.000031671 -3.9 0.00005 0.00005 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00003 0.00003 -3.8 0.00007 0.00007 0.00007 0.00006 0.00006 0.00006 0.00006 0.00005 0.00005 0.00005 -3.7 0.00011 0.00010 0.00010 0.00010 0.00009 0.00009 0.00008 0.00008 0.00008 0.00008 -3.6 0.00016 0.00015 0.00015 0.00014 0.00014 0.00013 0.00012 -3.5 0.00023 0.00022 0.00022 0.00021 0.00020 0.00019 -3.4 0.00034 0.00032 0.00031 0.00030 0.00029 0.00028 -3.3 0.00048 0.00047 0.00045 0.00043 0.00042 0.00040 0.00013 0.00019 0.00018 0.00017 0.00017 0.00027 0.00026 0.00025 0.00024 0.00039 0.00038 0.00036 0.00035 0.00012 0.00011 -3.2 0.00069 0.00066 0.00064 0.00062 0.00060 0.00058 0.00056 0.00054 0.00052 0.00050 -3.1 0.00097 0.00094 0.00090 0.00087 0.00084 0.00082 -3.0 0.00135 0.00131 0.00126 0.00122 0.00118 0.00114 0.00079 0.00111 0.00107 0.00103 0.00076 0.00074 0.00071 0.00100 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036