Problem help

**tilterino** · March 17th 2010, 03:36 PM

I would appreciate it if someone could help me solve or at least steer me in the right direction, thanks.

1)The daily high temperature at a particular resort destination during peak summer mounths follows a normal distribution with a mean of 28 deg and a s.d of 1.7 deg

- Find the probability that the high temperature for a random selected day during this time exceeds 30 deg.

- Suppose a random sample of 9 days is selected during these peak summers months and the mean daily high temperature is calculated.

Find MuX(bar) and omegaX(bar)

Describe the sampling of distribution X(bar)

What is the probability that this sample mean temperature falls between 27deg and 29deg

Thanks again.

**cpbrunner** · March 17th 2010, 06:54 PM

For the first problem:

You are given that the daily high temperatures follow a normal distribution with $\mu=28$ and $\sigma=1.7$ .

Let $X$ be the high temperature for a randomly selected day. To solve this problem, you'll need:
$P(X>30)=1-P(X\leq 30)=1-\Phi\left( \frac{30-28}{1.7}\right) \approx 1-\Phi(1.18) \approx 1-.881=.119$

So, the probability that a randomly selected day will have a high temperature greater than 30 is .119, or 11.9%.

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