Question

The quarterly returns for a group of 79 mutual funds with a mean of 1.1% and a standard deviation of 4.5% can be modeled by a normal model. based on the model N(0.011,0.045), what are the cutoff values for the:

a) highest 40% of these funds
b) lowest 20%?
c) middle 80%?
d) highest 80%?

Answer 1

To find the cutoff values for different percentiles of the funds, we use the z-scores based on the mean and standard deviation provided. For the highest 40%, lowest 20%, middle 80%, and highest 80%, we calculate the corresponding z-scores and then find the cutoff values using the formula z = (x - μ) / σ. These cutoff values define the ranges for each percentile.

Step-by-step explanation:

a) To find the cutoff values for the highest 40% of the funds, we need to find the z-scores corresponding to the 40th and 60th percentiles. For the 40th percentile, we find the z-score using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (x - 0.011) / 0.045. Solving for x, we find the cutoff value for the 40th percentile. For the 60th percentile, we repeat the process and find the cutoff value. These two cutoff values will give us the range for the highest 40% of the funds.

b) To find the cutoff values for the lowest 20% of the funds, we follow the same process as in part a, but now we are looking for the 20th percentile. We find the z-score and then solve for x to find the cutoff value.

c) To find the cutoff values for the middle 80% of the funds, we subtract the cutoff values for the lowest 20% from the cutoff values for the highest 40%. This will give us the range within which the middle 80% of the funds fall.

d) To find the cutoff values for the highest 80% of the funds, we subtract the cutoff value for the 20th percentile from the cutoff value for the 40th percentile. This will give us the range for the highest 80% of the funds.

Answer 2

Based on your question where the quarterly returns for a group of 79 mutual funds with a mean of 1.1% and the standard deviation of 4.5% can be modeled by a normal model so based on that data the possible answer among the choices is B.