The annual precipitation for one city is normally distributed with a mean of 329 inches and a
standard deviation of 2.6 inches. Find the probability that a randomly selected year will have more
than 323.8 inches of rain. Express the probability as a decimal. ??
You can work with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html
To find the probability that a randomly selected year will have more than 323.8 inches of rain, we need to find the area under the normal distribution curve to the right of the value 323.8.
Step 1: Standardize the value
To standardize the value of 323.8, we use the formula:
z = (x - μ) / σ
where
z is the standard score,
x is the given value,
μ is the mean of the distribution, and
σ is the standard deviation.
In this case, x = 323.8, μ = 329, and σ = 2.6.
Plugging in these values, we get:
z = (323.8 - 329) / 2.6 ≈ -2.077
Step 2: Use a standard normal distribution table or calculator
Next, we use a standard normal distribution table or calculator to find the area to the right of z = -2.077. This represents the probability that a randomly selected year will have more than 323.8 inches of rain.
Using a standard normal distribution table, we find that the area to the left of z = -2.077 is approximately 0.0192.
Since we want the area to the right, we subtract this value from 1:
1 - 0.0192 ≈ 0.9808
Therefore, the probability that a randomly selected year will have more than 323.8 inches of rain is approximately 0.9808 (expressed as a decimal).