Suppose that the annual rainfall in Ferndale, California, is known to be normally distributed, with a mean of 35.5 inches and a

Question

2 years ago

14

standard deviation of 2.5 inches. About 2.4% of the years, the annual rainfall will exceed how many inches? (Round your answer to one decimal place.)

1 answer:

erastovalidia [21] · Answer 1 · 2023-11-05T19:06:42+03:00

The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.

<h3>What is the average annual rainfall?</h3>

Generally, the equation for the probability is mathematically given as

$P( X < x) = p( Z < x - \mu / \sigma)$

Therefore

$P( X > x) = 0.021$

$P( X < x ) = 1 - 0.021\\\\\p( X < x) = 0.979$

$P( Z < x - \mu / \sigma) = 0.979$

The z score for the probability of 0.979 is 2.034, according to the table of z values.

$x - \mu / \sigma \\\\x= 2.034$

In the given equation, replace the values of mu and sigma with their respective values, and then solve for x.

$x - 35.5 / 2.5 \\x= 2.034$

In conclusion, The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.