Standard Deviation questions

[ak131313]

I have a question that has 3 parts to it. My problem is that I can't figure out the answer to the first part, which I need in order to figure out the answer to the other parts. I know how to answer the 2nd & 3rd parts, I just need help with the first part. Here is the question:

FActs: The mean hourly operating cost of a US Air 737 plane is $2,071. Assume that the hourly operating cost for the plane is normally distributed.

Part 1) If 11% of the hourly operating costs are $1,800 or less, what is the standard deviation of the hourly operating cost?

Any help would be appreciated. Thanks

 

[marcmtlca]

So, the idea here has to do with standardization of a normal. I will use some notation, if you are unfamiliar, please ask and i will explain. Anyhow,

suppose that some random quantity \(\displaystyle X\) follows a normal distribution with mean: \(\displaystyle \mu\) and variance \(\displaystyle \sigma^2\). (therefore the standard deviation is \(\displaystyle \sigma\). Then, it could be shown that the random quantity \(\displaystyle Z=\frac{X-\mu}{\sigma}\) follows a normal distribution with mean 0 and variance 1. This would be the distribution of the normal table that you guys have access to.

In your problem, X is hourly cost of a 737 plane and its mean is 2,071$. In otherwords, we have \(\displaystyle \mu=2071\) and we are looking to find \(\displaystyle \sigma\).

Now, in your normal table you have access to the following information:

\(\displaystyle P(X \le 1800)=P(Z \le z_{0})=0.11\)

You can find the value for \(\displaystyle z_0\) by finding the value of z in the table that gives you a probability of 0.11

you can then solve for \(\displaystyle \sigma\) by noting that

\(\displaystyle P[X\le 1800]=P[\frac{X-\mu}{\sigma} \le \frac{1800-\mu}{\sigma}]=P[Z \le \frac{1800-2071}{\sigma}=P[Z \le z_0]\)

solve \(\displaystyle z_0=\frac{1800-2071}{\sigma}\)