Laboratory rats commit an average of μ = 40 errors before they solve a standardized maze problem. The distribution of error scores is approximately normal with a standard deviation of σ = 8. A researcher is testing the effect of a new dietary supplement on intelligence. A newborn rat is selected and is given the supplement daily until it reaches maturity. The rat is then tested on the maze and finishes with a total of X = 24 errors. What is the probability that a regular rat (without the supplement) would solve the maze with a score less than or equal to X = 24 errors? Is it reasonable to conclude that the rat with the supplement is smarter than the vast majority of regular rats? Does it appear that the supplement has an effect on intelligence? Explain your answer.
Laboratory rats commit an average of μ = 40 errors before they solve a standardized maze problem. The distribution of error scores is approximately normal with a standard deviation of σ = 8. A researcher is testing the effect of a new dietary supplement on intelligence. A newborn rat is selected and is given the supplement daily until it reaches maturity. The rat is then tested on the maze and finishes with a total of X = 24 errors. What is the probability that a regular rat (without the supplement) would solve the maze with a score less than or equal to X = 24 errors? Is it reasonable to conclude that the rat with the supplement is smarter than the vast majority of regular rats? Does it appear that the supplement has an effect on intelligence? Explain your answer.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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Question
Laboratory rats commit an average of μ = 40 errors before they solve a standardized maze problem. The distribution of error scores is approximately normal with a standard deviation of σ = 8. A researcher is testing the effect of a new dietary supplement on intelligence. A newborn rat is selected and is given the supplement daily until it reaches maturity. The rat is then tested on the maze and finishes with a total of X = 24 errors.
- What is the
probability that a regular rat (without the supplement) would solve the maze with a score less than or equal to X = 24 errors? - Is it reasonable to conclude that the rat with the supplement is smarter than the vast majority of regular rats?
- Does it appear that the supplement has an effect on intelligence? Explain your answer.
Expert Solution
Step 1: Given information
Given that the regular laboratory rats follow a normal distribution with a mean being 40 and variance being 64, and a corresponding standard deviation being 8.
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- Is it reasonable to conclude that the rat with the supplement is smarter than the vast majority of rats?
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Is it reasonable to conclude that the rat with the supplement is smarter than the vast majority of rats
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