At a ski area in Vermont, the daytime high temperature is normally
distributed during January, with a mean of 22F and a standard
deviation of 10F You are planning to ski there this Jan.  What is the
probability that you will encounter daytime highs of
(a) 42F or higher? (b)15F or lower? (c) between 29F and 40F?

Hi musicboxx-ga,

These calculations all make use of the following formula, which
outputs a "z-value". This value can then be used to find the
cumulative probability of that z-value:

(Given value - Population Mean) / (Standard Deviation)

(a) z = (42 - 22)/10 = 2.2
   P(z) = 0.986096601
Since this value is the probability represents how likely the
temperature is to be below 42, we subtract it from 1 to obtain:

1 - 0.986096601 = 0.013903399

So there is a 1.3% chance that the temperature will be 42F or higher

(b) z = (15-22)/10 = -0.7
  P(z) = 0.241963578

So there is a 24.2% chance that the temperature will be 15F or lower

(c) z1 = (40-22)/10 = 1.8
  P(z1) = 0.964069734

    z2 = (29-22)/10 = 0.7
  P(z2) = 0.758036422

Since we are looking for the probability between these values, we
perform:
P(z1) - P(z2) = 0.964069734 - 0.758036422 = 0.206033312

So there is a 20.6% chance that the temperature will be between 29F
and 40F


Just for reference, I converted each z value to a P(z) value by using
the NORMSDIST(z) worksheet function in MS Excel, but there are many
ways to find this out, including z-distribution tables.

Hope that helps...ikf you have a problem understanding any of the
information above please post a clarification.

Cheers!

answerguru-ga

---

Clarification of Answer by answerguru-ga on 11 Dec 2002 22:49 PST

It seems I made a silly subtraction error for part (a) - the z value
should be 2 instead of 2.2, which results in a final answer of 0.0228.

Thanks to leapinglizard for spotting this error :)

answerguru-ga

Hi Musicboxx!

 Please see the answer I gave to your other question, as I think it
may answer both. :)

Let me know if you need any more help,

-Rebekah

I don't agree with answerguru's calculation for part (a).

We want

    1 - P((42-22)/10) = 1 - P(2)
                      = 1 - 0.9772
                      = 0.0228

leapinglizard