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# Normally distribution - Population Mean & SD

1. Assume that each energy type is produced by a process that is normally distributed and calculate the population mean and SD from the entire data set (1980 -2005).

2. Determine the probability that next year's production will exceed production in 1990 for each type.

Year Coal 2 Natural Gas 3 Crude Oil 4 Nuclear Electric Power "Renewable
Energy 5" Total Energy Production
1980 0.0 70.6 248.7 182.6 90.0 592.0
1981 0.0 56.4 201.7 159.4 83.7 501.1
1982 0.0 41.5 148.6 213.9 105.5 509.6
1983 0.0 35.6 113.0 161.4 94.6 404.6
1984 0.0 23.7 83.9 261.1 112.8 481.5
1985 0.0 20.1 66.5 249.2 114.6 450.3
1986 0.0 16.5 54.4 233.1 118.9 423.0
1987 0.0 15.2 48.0 196.0 108.8 368.0
1988 0.0 14.0 44.9 277.8 114.5 451.1
1989 0.0 13.9 42.3 221.4 233.6 511.1
1990 0.0 11.7 32.9 230.5 200.2 475.3
1991 0.0 8.4 27.4 215.0 214.4 465.2
1992 0.0 11.3 31.5 263.0 232.3 538.0
1993 0.0 11.7 32.5 271.9 218.3 534.4
1994 0.0 10.8 35.3 278.9 216.9 541.9
1995 0.0 9.3 33.0 302.0 221.5 565.8
1996 0.0 8.9 36.5 267.5 241.6 554.4
1997 0.0 8.8 37.0 241.0 232.8 519.6
1998 0.0 8.4 34.6 326.4 207.1 576.6
1999 0.0 8.6 28.4 329.5 206.1 572.6
2000 0.0 9.0 26.8 336.8 197.2 569.8
2001 0.0 7.9 25.7 330.0 160.7 524.2
2002 0.0 4.9 21.2 351.8 177.3 555.3
2003 0.0 4.6 18.9 322.8 191.9 538.2
2004 0.0 4.4 16.7 325.5 183.5 530.0
2005 0.0 3.7 15.0 300.1 192.7 511.4

See the attachment.

#### Solution Summary

The solution provides step by step method for the calculation of population mean, standard deviation and normal probability from a normally distributed data set. Formula for the calculation and Interpretations of the results are also included.

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