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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 Preview

Normally distributed - 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.

I need to know how to do this in Excel.

Thanks
1.
The formula used in excel are
Mean = AVERAGE (cell range)
Standard Deviation = STDEVP (cell range)

Coal Natural Gas Crude Oil Nuclear Electric Power Renewable Energy Total Energy Production
Mean 0 16.9 57.9 263.4 172.0 510.2
S.D. 0 16.13864699 56.96545234 54.87405271 52.31201381 55.34577723
2.
Coal
Let X be the next year's production. Given that X is normal with mean = 0 and standard deviation = 0. Standardizing the variable X using Z score and from normal distribution we have .
P (next year's ...

#### 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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