Standard Deviation question

[Pepsi]

Umm its tough to see so I'll write the question too...
The standard deviation of the annual growth rates of a mutual fund is an indicator of how volitile or risky the fund is. Determine the upper and lower limits of the annual growth rate for each fund, such that there is a 0.75 probability that the actual annual growth rate falls symmetrically about the mean within those limits, as showin in the diagram below.
(The Zscale from left to right starting at the bottom is, -x. mean, x)
Its end of the year practice so I forget a bit of things, but in the previous question I was to find the Mean and Standard deviation for the data provided for two separate funds. Now I'm just a bit stuck as to how I should go about this... Here's what I tryed
I'll just do for one fund right now cause once I figure out this one I can get the second easy.
Okay I take the mean collected in the first question, which is 4.2, and I simply make -x 3.5 (SD of .7) and x 4.9. Giving me the Lower and Upper bounds? I am so stuck if someone could lend a hand and work this out WITH ME that would be super.

 

[EnumaElish]

You have a mean and a standard deviation. So you know what the "bell curve" looks like because you know its location and spread. What you need to solve for is x, such that Prob(-x < r < x) = 0.75. If you standardize your variable r, you will have z = (r - μ)/σ. Then you can write Prob(-c < z < c) = 0.75, where c = (x - μ)/σ.

c is the multiple of your standard deviation that symmetrically bounds the growth rate with a probability of 0.75; it is the parameter you need to solve for.

 

[Architeuthis Dux]

I would suggest using the formula for calculating the upper and lower limits of a probability distribution, rather than simply using the mean and standard deviation from a previous question. This will ensure that your calculations are accurate and precise.

The formula for calculating the upper and lower limits with a given probability is:

Upper limit = Mean + (Zscore * Standard deviation)
Lower limit = Mean - (Zscore * Standard deviation)

In this case, the Zscore is 0.75, which corresponds to a probability of 0.75. So, the upper and lower limits for the annual growth rate of the mutual fund would be:

Upper limit = 4.2 + (0.75 * 0.7) = 4.725%
Lower limit = 4.2 - (0.75 * 0.7) = 3.675%

This means that there is a 75% probability that the actual annual growth rate falls between 3.675% and 4.725%, with the mean at 4.2%.

I would also suggest double checking your calculations for the mean and standard deviation from the previous question, just to ensure accuracy. If you are still having trouble, it may be helpful to consult a statistics textbook or seek assistance from a colleague or tutor.