8. The annual rainfall in Summer's Lush is approximately a normal random variable with mean 30 inches and variance 49 inches. a. What is the probability that next year's rainfall will exceed 30 inches? b. What is the probability that the yearly rainfalls in exactly 4 of the next 7 years will exceed 30 inches?
Added by Albert M.
Close
Step 1
Since the mean rainfall is 30 inches, the probability that next year's rainfall will exceed 30 inches is 0.5 or 50%. This is because, in a normal distribution, the probability of a random variable being greater than the mean is always 0.5. b. This is a binomial Show more…
Show all steps
Your feedback will help us improve your experience
Kari Hasz and 86 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The annual rainfall in Cincinnati is normally distributed with mean 40.14 inches and standard deviation 8.7 inches. (a) What is the probability this year's rainfall will exceed 42 inches? (5 points) (b) the yearly rainfalls in exactly 3 of the next 7 years will exceed 42 inches? (10 points) (c) What is the probability that the sum of the next 2 years' rainfall will exceed 84 inches? (5 points)
Shaiju T.
Suppose the yearly rainfall totals for a city in northern California follow a normal distribution, with a mean of 18 inches and a standard deviation of 6 inches. For a randomly selected year, what is the probability that total rainfall will be in each of the following intervals? Less than 10 inches. Greater than 30 inches. Between 15 and 21 inches. Greater than 35 inches
David N.
The annual rainfall in Cleveland, Ohio is approximately a normal random variable with mean $40.2$ inches and standard deviation $8.4$ inches. What is the probability that (a) next year's rainfall will exceed 44 inches; (b) the yearly rainfalls in exactly three of the next seven years will exceed 44 inches? Assume that if $A_{i}$ is the event that the rainfall exceeds 44 inches in year $i$ (from now), then the events $A_{i}, i \geq 1$, are independent.
Continuous Random Variables
Self-Test Problems And Exercises
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD