Given a normal distribution with =100 and =15, and given you select a sample of

Question

Given a normal distribution with =100 and =15, and given you select a sample of n=9, There is a 66% chance that X is above what value?Type an integer or decimal rounded to two decimal places as needed.)

My method

1-66%=44%=0.44then I find the closest value in the cumulative probability table0.4404marked in table 2Z value here is -0.15.

0.01 0.02 0.03 0.04. 0.05 0.06 0.07 0.08 0.09 0.00 6.0 0.00000000 5.5 0.000000019 5.0 0.000000287 4.5 0.000003398 4.0 0.00003167 3.9 0.00005 0.000050.000040.000040.000040.000040 000040.000030 000030.00003 3.8 0.0000 0.000070.000070.000060.000060.000060.000060 000050.000050 00005 3.7 0.00011 0.000100.000 100.000100.000090.00009 (0.000080 000080.000080.00008 3.6 0.00016 0.000150.000 150.000140.000 140.000 130.000130.000120.000120 00011 3.5 0.00023 0.000220.000220.000210 000200.000190.000190.000180.000 170.000 17 3.4 0.00034 0.000320.000310.000300.000290.000280 000270.000260 000250.00024 3.3 0.00048 0.000470.000450.000430.000420.000400.000 390.000 380 000360.00035 3.2 0.00069 0.000660.000640.000620.000600.000580 000560.0005400.000520.00050 3.1 0.00097 0.000940.000900.000870.000840.000820.000790 000760.000740.00071 0.00135 0.001310.001260.001220.00118 0.001140.00111 0.001070.001030.00100 3.0 2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 2.8 0.0026 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 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 00.0048 2.5 0.006 2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 2.3 0.010 2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 2.1 0.0179 2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 1.9 0.0287

Explanation / Answer

The corresponding z-value is z=-0.4124
Converting to raw score:
-0.4124 = (xbar-100)/(15/sqrt(9));
xbar = 5*(-0.4124)+100
xbar = 97.938

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