he annual precipitation for one city is normally distributed with a mean of 399 inches and a standard deviation of 3.3 inches. In what percentage of years is precipitation in the city between 392.4 inches and 405.6 inches?
Hard help?
you can use the same website I gave you in a previous post to answer your last two questions
this time use "area from a value" and enter the values in "between"
To find the percentage of years in which precipitation is between 392.4 inches and 405.6 inches, we need to calculate the probability within this range using the given mean and standard deviation.
First, we need to standardize the values by converting them to z-scores. The formula for calculating the z-score is:
z = (x - μ) / σ
Where:
z = z-score
x = value (in this case, the precipitation)
μ = mean
σ = standard deviation
For the lower value of 392.4 inches:
z1 = (392.4 - 399) / 3.3
For the upper value of 405.6 inches:
z2 = (405.6 - 399) / 3.3
Next, we use the standard normal distribution table or calculator to find the area under the curve between these two z-scores. The area represents the probability. The cumulative probability can be calculated by subtracting the cumulative probability of the lower z-score from the cumulative probability of the upper z-score:
P(392.4 < x < 405.6) = P(z1 < z < z2) = P(z2) - P(z1)
By looking up the z-scores in the standard normal distribution table or using a calculator, you can determine these probabilities. Subtracting the lower cumulative probability from the upper cumulative probability will give you the percentage of years in which precipitation is between 392.4 inches and 405.6 inches.