Mutual funds that specialize in the stock of natural resources companies showed considerable variation in their performance during the 12-month period ending July 2010. Consider the Rate of Return column in Table 5.5.3.
a. Find the average rate of return for these funds.
b. Find the standard deviation and briefly interpret this value.
c. How many of these mutual funds are within one standard deviation from the average? How does this compare to what you expect for a normal distribution?
d. How many of these mutual funds are within two standard deviations from the average? How does this compare to what you expect for a normal distribution?
e. How many of these mutual funds are within three standard deviations from the average? How does this compare to what you expect for a normal distribution?
f. Draw a histogram of this data set and indicate limits of one, two, and three standard deviations on the graph. Interpret your answers to parts c, d, and e in light of the shape of the distribution.

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TABLE 5.5.3 Natural Resources Mutual Funds: Rates of Return (12 months ending July 2010) and Assets (as of July 2010) Rate of Return 1.35% 5.83% 7.90% -097% 0.20% 3.28% 5.39% -4.01% -2.93% 1.10% 2.1 7% -1.91% 2.08% -2.10% un Assets (millions) 45.5 14.6 573.9 16.4 Columbia: Eng& Nat Rs:A Columbia: Eng&Nat Rs:C Columbia: Eng&Nat Rs2 Dreyfus Natural Res:A Dreyfus Natural Res B Dreyfus Natural Res;C Dreyfus Natural Res l Fidelity Adv Energy:A Fidelity Adv Energy; B Fidelity Adv Energy C Fidelity Adv Energy;l Fidelity Adv Energy;T Fidelity Sel Energy Fidelity Sel Nat Gas 4.3 1.8 202.2 41.8 84.6 23.8 205.0 1,746.5 854.9 (Continued) TABLE 5.5.3 Natural Resources Mutual Funds: Rates of Return (12 months ending July 2010) and Assets (as of July 2010)-contod Rate of Return -0.84% Assets (millions) ICON:Energy Invesco Enegy A Invesco Energy B Invesco Enegy C Invesco Energyinst Invesco Energydnv Invesco EnegyY Ivy EnergyA IvyEnergytB Ivy Energy Ivy Energyf Ivy.Enengyd Ivy Enegy:y Rydex:Energy FundA Rydex:Energy Fund:Adv 3.14% RydexcEnergy Fund C Rydex:Energy fund:Inv 3.68% RydexEnergy Scs A Rydex:Energy Svcs,Adv 1.60% Rydex: Energy SvcsC RydexEnergy Scsn 2.1 SAM Sust Waterinst Saratoga:Energy&BMA 5.01% Saratoga:Energy&BMB 6.80% Saratoga:Energy&BM,C 9.88% Saratoga:Energy&BMil 11.96% Vanguard Energy ix;Adin 3.00% W&R Adv Fnergy;A W&R Adv Energy;B W&R AdvEnergy:C W&R AdvEnergy;Y Ivy Energy 5978 84.8 167.9 0.35% -0.06% -1.45% 4.39% 2.81% -1.27% 4.95% -1.53% 1.65% -3.00% 0.08% 19.91% 178.0 -0.94% 5.83% 2.81%