Question

In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 4.1% with a standard deviation of 6.4%. If a normal model can be used to model​ them, what percent of the funds would you expect to be in each​ region? Use the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more precisely. Be sure to draw a picture first.

a) The Expected Percentage of returns that are 23.3% or more is ___%

b) The Expected Percentage of returns that are 4.1% or more is ____%

c) The Expected Percentage of returns that are between -2.3 and 10.5 is ____%

d) The Expected Percentage of returns that are -8.7% or less is _____%

Answer 1

a) 4.1 + 3 * 6.4 = 23.3

According to emperical rule about 99.7% of data falls within 3 standard deviation from the mean.

So 99.7%/2 = 49.85% of the data fall between 4.1 and 23.3.

So 50% - 49.85% = 0.15% of the data falls above 23.3.

So expected percentage of return = 64 * 0.0015 = 0.096

b) 50% of the data falls above and 50% of the data falls below the mean.

so 50% of the data falls above 4.1%.

So expected percentage of return that are 4.1% or more = 64 * 0.5000 = 32.

c) 4.1 - 6.4 = -2.3

4.1 + 6.4 = 10.5

According to emperical rule about 68% of data falls within 1 standard deviation from the mean.

So the expected percentage of returns = 64 * 0.68 = 43.52

d) 4.1 - 2 ^ 6.4 = -8.7

According to emperical rule about 95% of data falls within 2 standard deviation from the mean.

So 95%/2 = 47.5% of the data falls between 4.1 and -8.7

So 50% - 47.5% = 2.5% of the data falls below -8.7

The expected percentage of returns = 64 * 0.025 = 1.6