Question

According to the Normal model N(0.061,0.028​) describing mutual fund returns in the 1st quarter of​ 2013, determine what percentage of this group of funds you would expect to have the following returns. Complete parts​ (a) through​ (d) below.

​a) Over​ 6.8%?	​b) Between​ 0% and​ 7.6%?
​c) More than​ 1%?	​d) Less than​ 0%?

​a) The expected percentage of returns that are over​ 6.8% is _____%.

​(Type an integer or a decimal rounded to one decimal place as​ needed.)

​b) The expected percentage of returns that are between​ 0% and​ 7.6% is ______%.

​(Type an integer or a decimal rounded to one decimal place as​ needed.)

​c) The expected percentage of returns that are more than​ 1% is _____%.

​(Type an integer or a decimal rounded to one decimal place as​ needed.)

​d) The expected percentage of returns that are less than​ 0% is ______%.

​(Type an integer or a decimal rounded to one decimal place as​ needed.)

Answer 1

Solution: We are given mutual funds return follows normal distribution with mean, and standard deviation,

​a) The expected percentage of returns that are over​ 6.8% is

Answer: We are required to find here .

The z score is given below:

  

  

We have to find now . Using the standard normal table, we have:

or

Therefore, the expected percentage of returns that are over​ 6.8% is 40.1%.

​b) The expected percentage of returns that are between​ 0% and​ 7.6% is

Answer: We have to find here

Using the z score formula, we have:

Now using the standard normal distribution, we have:

  

   or

Therefore, the expected percentage of returns that are between​ 0% and​ 7.6% is 69.1%

​c) The expected percentage of returns that are more than​ 1% is

Answer: We are required to find here .

The z score is given below:

  

  

We have to find now . Using the standard normal table, we have:

or

Therefore, the expected percentage of returns that are more than​ 1% is 96.6%.

​d) The expected percentage of returns that are less than​ 0% is

Answer: We are required to find here .

The z score is given below:

  

  

We have to find now . Using the standard normal table, we have:

or

Therefore, the expected percentage of returns that are less than​ 0% is 1.5%.

​