5. The amount of rainfall in January in a certain city is normally distributed with a mean of 5 inches and a standard deviation of 0.4 inches. a. Find the value of the 25th percentile, rounded to the nearest tenth. b. What is the probability the rainfall in this city in January would be more than 5.5 inches? c. Would it be reasonable to expect the city to have less than 3 inches of rainfall in January? Explain. d. What is the probability the rainfall in this city in January would be between 4.8 inches and 5.3 inches? e. What would the probability that the mean of nine randomly selected Januarys in this city would be between 4.8 inches and 5.3 inches?
Added by Robert P.
Close
Step 1
Using a standard normal distribution table or calculator, we find that the z-score for the 25th percentile is approximately -0.674. We can then use the formula: z = (x - μ) / σ where x is the rainfall amount we want to find, μ is the mean (5 inches), and σ is Show more…
Show all steps
Your feedback will help us improve your experience
Clarissa Barr and 65 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
A weather forecaster predicts that the May rainfall in a local area will be between 2 and 9 inches but has no idea where within the interval the amount will be. Let x be the amount of May rainfall in the local area, and assume that X is uniformly distributed over the interval 2 to 9 inches (a) Calculate the expected May rainfall. (Round your answer to decimal place:) Hx (b) What is the probability that the observed May rainfall will fall within two standard deviations of the mean? Within one standard deviation of the mean? (Round all intermediate and final answers to 4 decimal places:) Probability of May rainfall will fall within two SD Probability of May rainfall will fall within one SD
Jacob F.
A weather forecaster predicts that the May rainfall in a local area will be between 1 and 6 inches but has no idea where within the interval the amount will be. Let x be the amount of May rainfall in the local area, and assume that x is uniformly distributed over the interval 1 to 6 inches. (a) Calculate the expected May rainfall. (Round your answer to 1 decimal place.) inches (b) What is the probability that the observed May rainfall will fall within two standard deviations of the mean? Within one standard deviation of the mean? (Round all intermediate and final answers to 4 decimal places.) Probability of May rainfall will fall within two SD Probability of May rainfall will fall within one SD
Robin C.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD