The percentage of years will have an annual rainfall of less than 44 inches 67%
A certain region is approximately normally distributed with mean 42.6 inches and standard deviation 6 inches.
a.) p(X < x).
Use Excel's norm.dist() function to calculate this probability directory or
convert x to a Z-score and use Excel's norm.s.dist() function or a Z table to find p(Z < z) or
convert x to a Z-score and look up the Z-score in a Z-table
norm.dist(x, mean, sd, True)
norm.dist(44, 41.6, 5.4, True). the 'True' tells excel to work with the cumulative normal distribution.
or
Z = (44 - 41.6)/5.4 = .44
p(Z <= .44) = .67 or 67%
b.) p(X > x). Use the above mentioned tools to calculated the p(X <= x) then calculate 1- p(X <= x). This will give you p(X > x)
c.) This is the "find the interval" part of the problem. Find p(X <= x_1), p(X <= x_2), then subtract the smaller from the larger probability. This will give you the probability of x's being in the interval state.
p(37 <= x <= 42) = p(X <= 42) - p(X <= 37)
Note: in a continuous distribution such as the normal distribution, we may assume continuity, so p(x > x) = p(x >= x), p(x < x) = p(x <= x)
Therefore, the percentage of years will have an annual rainfall of less than 44 inches 67%
To learn more about normal distribution refer here
https://brainly.com/question/4079902
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